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The area under velocity-time graph gives...

The area under velocity-time graph gives the displacement whereas the slope of velocity-time graph at any point gives acceleration at that point. Slope is +ve if the line makes an acute angle in the anticlockwise direction with respect to the positive direction along which the independent variable increases. From the calculus, we also know that the slope of the tangent to a y vs. x graph is given by `(dy)/(dx)` If `(dy)/(dx)` is +ve then y increases with x, otherwise it decreases. Consider two persons namely Ram, and Rahim, who have gone to picnic at a nice place. Finding a beautiful place they rush towards it simultaneously. Let us take the time when they start simultaneously at t= 0 and at this instant the position of Ram and Rahim be x = 0 and x = + 48, respectively. Ram maintains a uniform velocity of +10 m/s throughout the journey whereas Rahim starts from rest and continuously accelerates with + `1 m//s^(2)`
Q The velocity-time graph as well as the acceleration-time graph of Ram and Rahim are respectively,

A

(i) and (iv)

B

(ii) and (iv)

C

(i) and (v)

D

(iv) and (vi)

Text Solution

Verified by Experts

The correct Answer is:
C
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The area under velocity-time graph gives the displacement whereas the slope of velocity-time graph at any point gives acceleration at that point. Slope is +ve if the line makes an acute angle in the anticlockwise direction with respect to the positive direction along which the independent variable increases. From the calculus, we also know that the slope of the tangent to a y vs. x graph is given by (dy)/(dx) If (dy)/(dx) is +ve then y increases with x, otherwise it decreases. Consider two persons namely Ram, and Rahim, who have gone to picnic at a nice place. Finding a beautiful place they rush towards it simultaneously. Let us take the time when they start simultaneously at t= 0 and at this instant the position of Ram and Rahim be x = 0 and x = + 48, respectively. Ram maintains a uniform velocity of +10 m/s throughout the journey whereas Rahim starts from rest and continuously accelerates with + 1 m//s^(2) Q The position-time graph for the motions of Ram and Rahim is given by

The area under velocity-time graph gives the displacement whereas the slope of velocity-time graph at any point gives acceleration at that point. Slope is +ve if the line makes an acute angle in the anticlockwise direction with respect to the positive direction along which the independent variable increases. From the calculus, we also know that the slope of the tangent to a y vs. x graph is given by (dy)/(dx) If (dy)/(dx) is +ve then y increases with x, otherwise it decreases. Consider two persons namely Ram, and Rahim, who have gone to picnic at a nice place. Finding a beautiful place they rush towards it simultaneously. Let us take the time when they start simultaneously at t= 0 and at this instant the position of Ram and Rahim be x = 0 and x = + 48, respectively. Ram maintains a uniform velocity of +10 m/s throughout the journey whereas Rahim starts from rest and continuously accelerates with + 1 m//s^(2) Q Shown is a graph of either position or velocity-time graph Choose the correct alternative.

Knowledge Check

  • The area under a velocity-time graph gives :

    A
    Displacement
    B
    Change in velocity
    C
    Acceleration
    D
    Speed

  • Area under a velocity-time graph gives

    A
    the time taken by a moving object
    B
    the distance travelled by a moving object
    C
    the acceleration of moving object
    D
    the retardation of a moving object

  • The area under acceleration-time graph gives

    A
    Distance travelled
    B
    Change in acceleration
    C
    Force acting
    D
    Change in velocity

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    The slope of velocity-time graph for uniform motion of an object is

    The area under the acceleration-time (a-t) graph gives

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