Question

Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in one-dimensional motion (a) with zero speed at an instant may have non-zero acceleration at that instant (b) with zero speed may have non-zero velocity, (c) with constant speed must have zero acceleration, (d) with positive value of acceleration must be speeding up.

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Solution

(a)

When an object is thrown upwards then at highest point the speed of the object is zero but its acceleration is not zero. At the highest point, the acceleration of the ball is equal to the acceleration due to gravity. Hence, the given statement is true.

(b)

If an object has some velocity its speed can never be zero. Since the particle is moving in one dimensional motion, so the speed of the particle is equal to its own velocity. Hence, the given statement is false.

(c)

Acceleration is rate of change of velocity. If the velocity is constant then the change in velocity is zero and the acceleration is also zero. Hence, the given statement is true.

(d)

When the ball is thrown upwards it is under the acceleration due to gravity which is positive, but the speed is continuously decreases. Thus, the given statement is false.

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