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NEETPhysicsMotion in One Dimension

A rubber ball is dropped from a height h onto a hard floor. It hits the floor and bounces back perfectly elastically to the same height. Taking the downward direction as positive, which of the following correctly describes the velocity-time ( v-t ) graph for the motion of the ball from the moment it is dropped until it reaches its maximum height again?

Options

  1. ATwo parallel straight line segments with the same positive slope, separated by a sudden jump from a positive t
  2. BA continuous V-shaped graph entirely above the time axis, starting from the origin.
  3. CA continuous zig-zag graph with alternating positive and negative slopes, starting from the origin.
  4. DA single continuous straight line starting from a negative velocity, crossing the time axis to a positive velo

Correct answer

A. Two parallel straight line segments with the same positive slope, separated by a sudden jump from a positive t

Step-by-step solution

Let the downward direction be positive. The ball is dropped, so its initial velocity is zero. During the downward fall, the acceleration is a = +g (constant). The velocity increases linearly according to v = gt . This is represented by a straight line starting from the origin with a positive slope. Upon perfectly elastic impact with the floor, the velocity of the ball instantly reverses its direction but maintains its magnitude. Thus, the velocity abruptly changes from a positive value ( +v₀ ) to a negative value (

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