Answer to Question #258783 in Mechanics | Relativity for hloni

Question

. The acceleration of a particle P moving in a straight line is (t

2 − 9t + 18)ms−2

,

where t is the time in seconds.

(a) Find the values of t for which the acceleration is zero.

(b) It is given that when t = 3 the velocity of P is 9ms−1

.Find the velocity of P when t =0

(c) Show that the direction of motion of P changes before t = 1.

Answer 1

a)

$t^2-9t+18=0,$

$t=3 ~\text{or} ~t=6,$

b)

$v(t)=\int adt=\frac 13t^3-\frac 92t^2+18t+C,$

$v(3)=23.5+C=9,\implies$ $C=-14.5,$

$v(0)=-14.5~\frac ms,$

c)

$\frac 13t^3-\frac 92t^2+18t-14.5=0,$

$t\approx 1.07>1.$