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.
Step 1: (a)The particle will be moving along positive x-direction the only if t > sint
Hence, x(t)=t-sin t
Velocity, v(t) = dx(t)dt = 1 − cost Acceleration, a(t) = dvdt = sint When t = 0; x(t) = 0 When t = π; x(t) = π>0 When t = 0; x(t) = 2π>0
Step 2: (b) Equation can be represented by
x(t) = sintv = ddtx(t) = cost
As displacement and velocity are involving sint and cost hence, these equations represent periodically.
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