A particle moves in such a way that its displacement at time t seconds is given by
s(t)=At3+Bt2+Ct+D,
where A,B,C,D are constants.
a. (i) Obtain expressions for the velocity v(t) and acceleration a(t) of the particle.
b. (ii) Show that the acceleration is not uniform when A=0.
c. (iii) Find the condition(s) on A and B under which the particle will move with constant acceleration.
d. (iv) For the specific case A=1,B=−3,C=2,D=0, determine the time at which the acceleration attains its minimum value.