Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

A particle moves along a straight line such that its position $x$ at any time $t$ is $x equals 6 t to the power of 2 end exponent minus t to the power of 3 end exponent.$ Where $x$ in metre ant $t$ is in second, then

At $t = 0$ acceleration is $12 {m s}^{- 2}$
$x - t$ curve has maximum at 4 s
Both [a] and [b] are wrong
Both [a] and [b] are correct

The correct answer is: Both [a] and [b] are correct

Given, $x equals 6 t to the power of 2 end exponent minus t to the power of 3 end exponent$
$fraction numerator d x over denominator d t end fraction equals 12 t minus 3 t to the power of 2 end exponent blank open parentheses i close parentheses$
$fraction numerator d x over denominator d t end fraction equals 0 rightwards double arrow t equals 4 blank s$
Now, again differentiating Eq. (i), we get
$fraction numerator d to the power of 2 end exponent x over denominator d t to the power of 2 end exponent end fraction equals 12 minus 6 t equals 12 minus 6 open parentheses 4 close parentheses equals negative 12$
Since, $fraction numerator d to the power of 2 end exponent x over denominator d t to the power of 2 end exponent end fraction$ is negative, hence $t equals 4 blank s$ gives the maximum value for $x minus t$ curve.
Moreover, acceleration $a equals fraction numerator d to the power of 2 end exponent x over denominator x t to the power of 2 end exponent end fraction comma blank a t blank t equals 0 comma fraction numerator d to the power of 2 end exponent x over denominator d t to the power of 2 end exponent end fraction equals 12 blank m s to the power of negative 2 end exponent$

Related Questions to study

A Body moves 6 $m blank$ north.8 $m$ east and 10 $blank m$ vertically upwards, what is its resultant displacement from initial position

A Body moves 6 $m blank$ north.8 $m$ east and 10 $blank m$ vertically upwards, what is its resultant displacement from initial position

Physics-General

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $6 blank s e c$ are respectively

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $6 blank s e c$ are respectively
Physics-General

A body starting from rest moves with uniform acceleration. The distance covered by the body in time $t$ is proportional to

A body starting from rest moves with uniform acceleration. The distance covered by the body in time $t$ is proportional to

Physics-General

parallel

A projectile is fired vertically upwards with an initial velocity $u$ . After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity is

A projectile is fired vertically upwards with an initial velocity $u$ . After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity is

Physics-General

Free fall of an object (in vacuum) is a case of motion with

Free fall of an object (in vacuum) is a case of motion with

Physics-General

A car moves a distance of $200 blank m$ . It covers first half of the distance at speed $60 blank k m h to the power of negative 1 end exponent$ and the second half at speed $v$ . If the average speed is $40 blank k m h to the power of negative 1 end exponent$ , the value of $v$ is

A car moves a distance of $200 blank m$ . It covers first half of the distance at speed $60 blank k m h to the power of negative 1 end exponent$ and the second half at speed $v$ . If the average speed is $40 blank k m h to the power of negative 1 end exponent$ , the value of $v$ is

Physics-General

parallel

A ball is dropped on the floor from a height of $10 blank m$ . It rebounds to a height of $2.5 m$ . If the ball is in contact with the floor for $0.01$ sec, the average acceleration during contact is

A ball is dropped on the floor from a height of $10 blank m$ . It rebounds to a height of $2.5 m$ . If the ball is in contact with the floor for $0.01$ sec, the average acceleration during contact is

Physics-General

A particle moving with a uniform acceleration travels 24 $m$ and 64 $m blank$ in the first two consecutive intervals of 4 $s e c$ each.
Its initial velocity is

A particle moving with a uniform acceleration travels 24 $m$ and 64 $m blank$ in the first two consecutive intervals of 4 $s e c$ each.
Its initial velocity is

Physics-General

A bullet is fired with a speed of $1000 blank m divided by s e c$ in order to hit a target $100 blank m$ away. If $g equals 10 blank m divided by s to the power of 2 end exponent$ , the gun should be aimed

A bullet is fired with a speed of $1000 blank m divided by s e c$ in order to hit a target $100 blank m$ away. If $g equals 10 blank m divided by s to the power of 2 end exponent$ , the gun should be aimed

Physics-General

parallel

From an elevated point $A$ , a stone is projected vertically upwards. When the stone reaches a distance $h$ below $A$ , its velocity is double of what was at a height above $A$ . The greatest height attained by the stone is

From an elevated point $A$ , a stone is projected vertically upwards. When the stone reaches a distance $h$ below $A$ , its velocity is double of what was at a height above $A$ . The greatest height attained by the stone is

Physics-General

Two bodies being a free fall from rest, from the same height 2s apart. How long after the first body begins to fall the two bodies will be 40m apart? (Take $g equals 10 m s to the power of negative 2 end exponent$ )

Two bodies being a free fall from rest, from the same height 2s apart. How long after the first body begins to fall the two bodies will be 40m apart? (Take $g equals 10 m s to the power of negative 2 end exponent$ )

Physics-General

The velocity of a body of mass 20 kg decreases from $20 blank m s to the power of negative 1 end exponent t o blank 5 blank m s to the power of negative 1 end exponent$ in a distance of 100 m. Force on the body is

The velocity of a body of mass 20 kg decreases from $20 blank m s to the power of negative 1 end exponent t o blank 5 blank m s to the power of negative 1 end exponent$ in a distance of 100 m. Force on the body is

Physics-General

parallel

The displacement of the particle varies with time according to the relation $x equals fraction numerator k over denominator b end fraction open square brackets 1 minus e to the power of negative b t end exponent close square brackets.$ Then the velocity of the particle is

The displacement of the particle varies with time according to the relation $x equals fraction numerator k over denominator b end fraction open square brackets 1 minus e to the power of negative b t end exponent close square brackets.$ Then the velocity of the particle is

Physics-General

A train starts from station with an acceleration $1 m s to the power of negative 2 end exponent$ . A boy is 48 m behind the train with a constant velocity $10 m s to the power of negative 1 end exponent$ , the minimum time after which the boy will catch the train is

A train starts from station with an acceleration $1 m s to the power of negative 2 end exponent$ . A boy is 48 m behind the train with a constant velocity $10 m s to the power of negative 1 end exponent$ , the minimum time after which the boy will catch the train is

Physics-General

A particle starts from rest at $t equals 0$ and undergoes an acceleration a in $m s to the power of negative 2 end exponent$ with time $t$ in seconds which is as shown Which one of the following plot represents velocity $V$ in $m s to the power of negative 1 end exponent$ versus time $t$ in seconds

A particle starts from rest at $t equals 0$ and undergoes an acceleration a in $m s to the power of negative 2 end exponent$ with time $t$ in seconds which is as shown Which one of the following plot represents velocity $V$ in $m s to the power of negative 1 end exponent$ versus time $t$ in seconds

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.