Question

The velocity of a particle which moves along

the s-axis is given by

V=2 - 4t + 58312

, Where t is in seconds and v is

in meters per second. Evaluate the position s,

velocity v, and acceleration a when t = 3 s. The

particle is at the position S, = 3 m when t=0.

Answer 1

$v=2-4t+5t^2,$

$s=2t-2t^2+\frac 53t^3+c,$

$s(0)=c=3,$

$s=2t-2t^2+\frac 53 t^3+3,$

$s(3)=36~m,$

$v(3)=35~\frac m{s},$

$a=10t-4,$

$a(3)=26~\frac m{s^2}.$