The displacement of a body moving along the –axis is given by metres

MATHEMATICS · Subjective · A Level · Mathematics · Kinematics · Kinematics

Problem

The displacement of a body moving along the

x

–axis is given by

x(t)=2\sin(4t)+3t^{2}

metres. (i) Derive expressions for its instantaneous velocity

v(t)

and instantaneous acceleration

a(t)

. (ii) Find the time(s) in the interval

0\le t\le 2\,\text{s}

when the instantaneous velocity becomes zero. (iii) Determine the acceleration of the body at each of those time instants.