Let a body move along the saxis with its position given as s

Let a body move along the s-axis with its position given as s(t)=t^3-6t^2+9t in meters, with t in seconds. Find each of the following (5 pts. each): (a) The velocity v and acceleration a. (b) a when v = 0. (c) The speed when a = 0.

Solution

s= t³-6t²+9t

a. Velocity, ds/dt= 3t²-12t +9

acceleration, dv/dt= 6t-12

b.

v=0

3t²-12t +9=0

t²-4t+3=0

(t-1)(t-3)=0

t=1, 3

at t=1, a=6(1)-12=-6 m/sec²

at t=3, a= 6(3)-12=6 m/sec²

c.a=0

6t-12=0

t=2 sec

v(2)= 3(2)²-12(2)+9=-3m/sec