Ncert Exercises & Solutions

Give examples of a one-dimensional motion where

(a) the particle moving along positive x-direction comes to rest periodically and moves forward.

(b) the particle moving along positive x-direction comes to rest periodically and moves backward.

Hint: For periodic motion, its equation must have a sine or cosine function.

Step 1: (a)The particle will be moving along positive x-direction the only if t > sint

Hence, x(t)=t-sin t

$\begin{array}{l} Velocity, v (t) = \frac{dx (t)}{dt} = 1 - cost \\ Acceleration, a (t) = \frac{dv}{dt} = sint \\ When t = 0; x (t) = 0 \\ When t = π; x (t) = π > 0 \\ When t = 0; x (t) = 2 π > 0 \end{array}$

Step 2: (b) Equation can be represented by

$\begin{array}{l} x (t) = sint \\ v = \frac{d}{dt} x (t) = cost \end{array}$

As displacement and velocity are involving sint and cost hence, these equations represent periodically.

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