A particle moves in such a way that its displacement at time seconds is given by…

MATHEMATICS · Multi-part · A Level · Mathematics · Kinematics · Kinematics

Problem

A particle moves in such a way that its displacement at time

t

seconds is given by

s(t)=At^{3}+Bt^{2}+Ct+D,

where

A,\,B,\,C,\,D

are constants. (i) Obtain expressions for the velocity

v(t)

and acceleration

a(t)

of the particle. (ii) Show that the acceleration is not uniform when

A\ne0

. (iii) Find the condition(s) on

A

and

B

under which the particle will move with constant acceleration. (iv) For the specific case

A=1,\;B=-3,\;C=2,\;D=0

, determine the time at which the acceleration attains its minimum value.