The displacement of a toy train moving on a straight track is given by x(t)=10…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

The displacement

x

of a toy train moving on a straight track is given by

x(t)=10\sin\!(0.5t)+6\cos\!(0.5t)\;\text{m},

where

t

is the time in seconds. (i) Derive the expression for the instantaneous velocity

v(t)

of the train. (ii) Compute the instantaneous velocity and speed at

t=4\,\text{s}

. (iii) Determine the earliest positive time (other than

t=0

) at which the train comes momentarily to rest.