Physics-
General
Easy

Question

A point initially at rest moves along x minusaxis. Its acceleration varies with time as a equals open parentheses 6 t plus 5 close parentheses m s to the power of negative 2 end exponent. If it starts from origin, the distance covered in 2 s is

  1. 20 m  
  2. 18 m  
  3. 16 m  
  4. 25 m  

The correct answer is: 18 m


    Given, blank a equals fraction numerator d v over denominator d t end fraction equals 6 t plus 5
    Or blank d v equals open parentheses 6 t plus 5 close parentheses blank d t
    Integrating, we get
    not stretchy integral subscript 0 end subscript superscript v end superscript d v equals not stretchy integral subscript 0 end subscript superscript t end superscript open parentheses 6 t plus 5 close parentheses blank d t
    Orblank v equals open parentheses fraction numerator 6 t to the power of 2 end exponent over denominator 2 end fraction plus 5 t close parentheses
    Again blank v equals fraction numerator d s over denominator d t end fraction
    therefore d s equals open parentheses fraction numerator 6 t to the power of 2 end exponent over denominator 2 end fraction plus 5 t close parentheses blank d t
    Integrating again, we get
    not stretchy integral subscript 0 end subscript superscript s end superscript d s equals not stretchy integral subscript 0 end subscript superscript t end superscript open parentheses fraction numerator 6 t to the power of 2 end exponent over denominator 2 end fraction plus 5 t close parentheses d t
    therefore s equals fraction numerator 3 t to the power of 3 end exponent over denominator 3 end fraction plus fraction numerator 5 t to the power of 2 end exponent over denominator 2 end fraction
    When, t equals 2 blank s comma blank s equals 3 cross times fraction numerator 2 to the power of 3 end exponent over denominator 3 end fraction plus fraction numerator 5 blank cross times 2 to the power of 2 end exponent over denominator 2 end fraction equals 3 cross times fraction numerator 8 over denominator 3 end fraction plus fraction numerator 5 blank cross times 4 over denominator 2 end fraction
    equals 8 plus 10 equals 18 blank m

    Related Questions to study

    General
    Physics-

    Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

    Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph
    Physics-General

    General
    Physics-

    A bird flies for 4 blank s with a velocity of open vertical bar t minus 2 close vertical bar m divided by s in a straight line, where t is time in seconds. It covers a distance of

    A bird flies for 4 blank s with a velocity of open vertical bar t minus 2 close vertical bar m divided by s in a straight line, where t is time in seconds. It covers a distance of

    Physics-General
    General
    Physics-

    A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

    A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is
    Physics-General

    parallel
    General
    Physics-

    An automobile travelling with a speed of 60 blank k m h to the power of negative 1 end exponent comma can brake to stop within a distance of 20 m. if the car is going twice as fast, i e. comma blank 120 blank k m h to the power of negative 1 end exponent comma the stopping distance will be

    An automobile travelling with a speed of 60 blank k m h to the power of negative 1 end exponent comma can brake to stop within a distance of 20 m. if the car is going twice as fast, i e. comma blank 120 blank k m h to the power of negative 1 end exponent comma the stopping distance will be

    Physics-General
    General
    Physics-

    A particle moves along x minusaxis in such a way that its coordinate open parentheses x close parentheses varies with time t according to the expression x equals 2 minus 5 t plus 6 t to the power of 2 end exponent m comma the initial velocity of the particle is

    A particle moves along x minusaxis in such a way that its coordinate open parentheses x close parentheses varies with time t according to the expression x equals 2 minus 5 t plus 6 t to the power of 2 end exponent m comma the initial velocity of the particle is

    Physics-General
    General
    Physics-

    A ball released from the top of a tower travels fraction numerator 11 over denominator 36 end fractionof the height of the tower in the last second of its journey. The height of the tower is (Take g equals 10 equals m s to the power of negative 2 end exponent)

    A ball released from the top of a tower travels fraction numerator 11 over denominator 36 end fractionof the height of the tower in the last second of its journey. The height of the tower is (Take g equals 10 equals m s to the power of negative 2 end exponent)

    Physics-General
    parallel
    General
    Physics-

    A particle moves along a straight line such that its displacement at any time t is given by S equals t to the power of 3 end exponent minus 6 t to the power of 2 end exponent plus 3 t plus 4 blank m e t r e s
    The velocity when the acceleration is zero is

    A particle moves along a straight line such that its displacement at any time t is given by S equals t to the power of 3 end exponent minus 6 t to the power of 2 end exponent plus 3 t plus 4 blank m e t r e s
    The velocity when the acceleration is zero is

    Physics-General
    General
    Physics-

    A body is thrown vertically upwards with a velocity u.Find the true statement from the following

    A body is thrown vertically upwards with a velocity u.Find the true statement from the following

    Physics-General
    General
    Physics-

    Two cars move in the same direction along parallel roads. One of them is a 100 m long travelling with a velocity of 7.5 m s to the power of negative 1 end exponent. How long will it take for the first car to overtake the second car?

    Two cars move in the same direction along parallel roads. One of them is a 100 m long travelling with a velocity of 7.5 m s to the power of negative 1 end exponent. How long will it take for the first car to overtake the second car?

    Physics-General
    parallel
    General
    Physics-

    A particle has an initial velocity of 3 stack i with hat on top plus 4 stack j with hat on top and an acceleration of 0.4 stack i with hat on top plus 0.3 stack j with hat on top. Its speed after 10 blank s is

    A particle has an initial velocity of 3 stack i with hat on top plus 4 stack j with hat on top and an acceleration of 0.4 stack i with hat on top plus 0.3 stack j with hat on top. Its speed after 10 blank s is

    Physics-General
    General
    Physics-

    A body starts to fall freely under gravity. The distance covered by it in first, second and third s e c o n d are in ratio

    A body starts to fall freely under gravity. The distance covered by it in first, second and third s e c o n d are in ratio

    Physics-General
    General
    Physics-

    A particle located at x equals 0 at time t equals 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v equals a square root of x. The displacement of the particle varies with time as

    A particle located at x equals 0 at time t equals 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v equals a square root of x. The displacement of the particle varies with time as

    Physics-General
    parallel
    General
    Physics-

    A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate fraction numerator f over denominator 2 end fraction to come to rest. If the total distance traversed is 15 blank S, then

    A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate fraction numerator f over denominator 2 end fraction to come to rest. If the total distance traversed is 15 blank S, then

    Physics-General
    General
    Physics-

    The motion of a particle is described by the equation u equals a t. The distance travelled by the particle in the first 4 seconds

    The motion of a particle is described by the equation u equals a t. The distance travelled by the particle in the first 4 seconds

    Physics-General
    General
    Physics-

    A car travels half the distance with constant velocity of 40 blank k m p h and the remaining half with a constant velocity of 60 blank k m p h. The average velocity of the car in k m p h is

    A car travels half the distance with constant velocity of 40 blank k m p h and the remaining half with a constant velocity of 60 blank k m p h. The average velocity of the car in k m p h is

    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.