Mathematics

Problem

The position

s

(in metres) of a bus moving along a straight road after

t

seconds is given by

s(t)=t\sin t + t

. a. (i) Find the velocity

v(t)

of the bus at any time

t

. b. (ii) Calculate the instantaneous velocity when

t=\dfrac{\pi}{4}

s. c. (iii) Write the equation of the tangent to the graph of

s

versus

t

at the point corresponding to

t=\dfrac{\pi}{4}