Maths-

General

Easy

Question

The displacement of a particle in time ‘t’ is given by S = t³ – t² – 8t – 18. The acceleration of the particle when its velocity vanishes is

10
10 units /sec²
5 units/sec²
20 units/sec²

hint Hint:

We are given the equation of displacement of a particle. We have to find the value of its acceleration at the point where velocity vanishes i.e. becomes zero. Acceleration is second order derivative of the equation and velocity is first order derivative of displacement.

The correct answer is: 10 units /sec²

The given expression is s = t³ - t² - 8t - 18.
To get the velocity we will differentiate the above equation w.r.t "t" . And to find the point at which it's vanishing, we will equate the derivate with zero.
$s space equals space t cubed space minus space t squared space minus 8 t space minus 18 fraction numerator d s over denominator d t end fraction equals 3 t squared space minus 2 t space minus space 8 T h i s space i s space t h e space e q u a t i o n space o f space v e l o c i t y. space$
$W e space w i l l space e q u a t e space t h e space e q u a t i o n space w i t h space z e r o 0 space equals space 3 t squared space minus 2 t space minus 8 0 space equals space 3 t squared space minus space 6 t space plus 4 t space minus space 8 space space space space space space... left parenthesis f a c t o r i z a t i o n right parenthesis 0 space equals space 3 t left parenthesis t space minus space 2 right parenthesis space plus space 4 left parenthesis t space space minus space 2 right parenthesis R e a r r a n g i n g space t h e space a b o v e space e q u a t i o n left parenthesis 3 t space plus space 4 right parenthesis left parenthesis t space minus 2 right parenthesis space equals space 0 S o comma space 3 t plus space 4 space equals space 0 space o r space t space minus space 2 space equals space 0 t space not equal to negative 4 over 3 space a s space t i m e space c a n n o t space b e space n e g a t i v e t space equals space 2$
The point at which velocity is vanishing is t = 2
Now, we will find the equation for acceleration by taking the second order derivative of displacement.
$fraction numerator d squared s over denominator d t squared end fraction equals space 6 t space minus space 2 L e t space u s space d e n o t e space a c c e l e r a t i o n space b y space " a " a space equals space 6 t space minus space 2$
We will substitute the value of t = 2 to find the acceleration at required point.
a = 6(2) - 2
= 12 - 2
= 10 units/sec²
So, the acceleration at the point where velocity vanishes is 10units/sec²

For such questions, we should know relation between displacement, velocity and time. We should also know how to find first and second order derivate.

If $S subscript n end subscript equals stretchy sum from k equals 1 to n of a subscript k end subscript$ and $stack l i m with n rightwards arrow infinity below a subscript n end subscript equals a comma$ then $stack l i m with n rightwards arrow infinity below fraction numerator S subscript n plus 1 end subscript minus S subscript n end subscript over denominator square root of stretchy sum from k equals 1 to n of k end root end fraction$ is equal to

Maths-General

General

Maths-

$stack l i m with n rightwards arrow infinity below open square brackets fraction numerator 1 over denominator n to the power of 3 end exponent plus 1 end fraction plus fraction numerator 4 over denominator n to the power of 3 end exponent plus 1 end fraction plus fraction numerator 9 over denominator n to the power of 3 end exponent plus 1 end fraction plus horizontal ellipsis horizontal ellipsis. plus fraction numerator n to the power of 2 end exponent over denominator n to the power of 3 end exponent plus 1 end fraction close square brackets equals$

Maths-General

General

Maths-

$stack l i m with x rightwards arrow 0 below fraction numerator square root of 1 plus x end root minus square root of 1 minus x end root over denominator sin to the power of negative 1 end exponent invisible function application x end fraction equals$

Maths-General

General

Physics-

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as $mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis$ . The optical path length of ray R will be

Physics-General

General

Physics-

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from $S subscript 1 end subscript$ and $S subscript 2 end subscript$ . The distance between slits is 1 mm.

Physics-General

General

Physics-

In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

Physics-General

General

Physics-

An YDSE is carried out in a liquid of refractive index $mu equals 1.3$ and a thin film of air is formed in front of the lower slit as shown in the figure. If a maxima of third order is formed at the origin O, find the thickness of the air film. The wavelength of light in air is $lambda subscript 0 end subscript equals 0.78 mu m$ and D/d=1000.

Physics-General

General

Physics-

Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

Physics-General

General

Physics-

Two coherent narrow slits emitting light of wavelength $lambda$ in the same phase are placed parallel to each other at a small separation of $2 lambda$ . The light is collected on a screen S which is placed at a distance $D left parenthesis much greater-than lambda right parenthesis$ from the slit $S subscript 1 end subscript$ as shown in figure. Find the finite distance x such that the intensity of P is equal to intensity at O.

Physics-General

General

Physics-

Consider the arrangement shown in figure. By some mechanism, the separation between the slits $S subscript 3 end subscript$ and $S subscript 4 end subscript$ can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of $S subscript 1 end subscript S subscript 2 end subscript$ and $S subscript 3 end subscript S subscript 4 end subscript$ . When $z equals fraction numerator D lambda over denominator 2 blank d end fraction$ , the intensity measured at P is I. Find this intensity when z is equal to

1) $fraction numerator D lambda over denominator d end fraction$ ,
2) $fraction numerator 3 D lambda over denominator 2 blank d end fraction$ , and
3) $fraction numerator 2 D lambda over denominator d end fraction$ .

Physics-General

General

Maths-

$stack l i m with x rightwards arrow pi divided by 2 below fraction numerator a to the power of cot invisible function application x end exponent minus a to the power of cos invisible function application x end exponent over denominator c o t invisible function application x minus c o s invisible function application x end fraction equals$

Maths-General

General

Physics-

In Young's double slit experiment $S subscript 1 end subscript$ and $S subscript 2 end subscript$ are two slits. Films of thicknesses $t subscript 1 end subscript$ and $t subscript 2 end subscript$ and refractive indices $m subscript 1 end subscript$ and $m subscript 2 end subscript$ are placed in front of $S subscript 1 end subscript$ and $S subscript 2 end subscript$ respectively. If $m subscript 1 end subscript t subscript 1 end subscript equals m subscript 2 end subscript t subscript 2 end subscript$ , then the central maximum will :

Physics-General

General

Physics-

Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

Physics-General

General

Physics-

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Physics-General

General

Physics-

Bright colours exhibited by spider's web, exposed to sunlight are due to

Physics-General

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

The displacement of a particle in time ‘t’ is given by S = t³ – t² – 8t – 18. The acceleration of the particle when its velocity vanishes is

10
10 units /sec²
5 units/sec²
20 units/sec²

We are given the equation of displacement of a particle. We have to find the value of its acceleration at the point where velocity vanishes i.e. becomes zero. Acceleration is second order derivative of the equation and velocity is first order derivative of displacement.

The correct answer is: 10 units /sec²

Related Questions to study

$stack l i m with x rightwards arrow 0 below fraction numerator square root of 1 plus x end root minus square root of 1 minus x end root over denominator sin to the power of negative 1 end exponent invisible function application x end fraction equals$

$stack l i m with x rightwards arrow 0 below fraction numerator square root of 1 plus x end root minus square root of 1 minus x end root over denominator sin to the power of negative 1 end exponent invisible function application x end fraction equals$

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as $mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis$ . The optical path length of ray R will be

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as $mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis$ . The optical path length of ray R will be

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from $S subscript 1 end subscript$ and $S subscript 2 end subscript$ . The distance between slits is 1 mm.

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from $S subscript 1 end subscript$ and $S subscript 2 end subscript$ . The distance between slits is 1 mm.

In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Bright colours exhibited by spider's web, exposed to sunlight are due to

Bright colours exhibited by spider's web, exposed to sunlight are due to

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

Follow Us at

Support

Download App

Courses

Quick Links

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

The displacement of a particle in time ‘t’ is given by S = t3 – t2 – 8t – 18. The acceleration of the particle when its velocity vanishes is

10 10 units /sec2 5 units/sec2 20 units/sec2

We are given the equation of displacement of a particle. We have to find the value of its acceleration at the point where velocity vanishes i.e. becomes zero. Acceleration is second order derivative of the equation and velocity is first order derivative of displacement.

The correct answer is: 10 units /sec2

Related Questions to study

If and then is equal to

If and then is equal to

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as . The optical path length of ray R will be

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as . The optical path length of ray R will be

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from and . The distance between slits is 1 mm.

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from and . The distance between slits is 1 mm.

In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

An YDSE is carried out in a liquid of refractive index and a thin film of air is formed in front of the lower slit as shown in the figure. If a maxima of third order is formed at the origin O, find the thickness of the air film. The wavelength of light in air is and D/d=1000.

An YDSE is carried out in a liquid of refractive index and a thin film of air is formed in front of the lower slit as shown in the figure. If a maxima of third order is formed at the origin O, find the thickness of the air film. The wavelength of light in air is and D/d=1000.

Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

In Young's double slit experiment and are two slits. Films of thicknesses and and refractive indices and are placed in front of and respectively. If , then the central maximum will :

In Young's double slit experiment and are two slits. Films of thicknesses and and refractive indices and are placed in front of and respectively. If , then the central maximum will :

Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Bright colours exhibited by spider's web, exposed to sunlight are due to

Bright colours exhibited by spider's web, exposed to sunlight are due to

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

The displacement of a particle in time ‘t’ is given by S = t³ – t² – 8t – 18. The acceleration of the particle when its velocity vanishes is

10
10 units /sec²
5 units/sec²
20 units/sec²

The correct answer is: 10 units /sec²

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as $mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis$ . The optical path length of ray R will be

The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as $mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis$ . The optical path length of ray R will be

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from $S subscript 1 end subscript$ and $S subscript 2 end subscript$ . The distance between slits is 1 mm.

A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from $S subscript 1 end subscript$ and $S subscript 2 end subscript$ . The distance between slits is 1 mm.