The displacement (in metres) of a particle moving in a straight line after seconds is…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The displacement (in metres) of a particle moving in a straight line after

t

seconds is given by

s(t)=\frac{(3t^{2}-2t)\cos t}{t+2}+\frac{(t^{2}+1)\sin t}{t^{2}}.

(i) Obtain the velocity

v(t)

of the particle. (ii) Find the acceleration

a(t)

and hence determine

a(\pi)

. (iii) State, with reason, whether the particle is speeding up or slowing down at

t=\pi