Question

A particle p moves in a straight line with a velocity v m/sec that is given by v=4t^2-1 where t is the time after passing through a fixed point O on the line .find the instant when p is instantaneously at rest .also find at that instant ,displacement of p from O.

Answer 1

to be at rest, v = 0
4t^2 - 1 = 0
4t^2 = 1
t^2 = 1/4
t = 1/2

let the displacement be s
s = (4/3)t^3 - t + c
assume that when t = 0 , s=0 , then c =0

s= (4/3)t^2 - t
when t = 1/2
s = (4/3)(1/4) - 1/2
= 1/3 - 1/2
= -1/6

the object is 1/6 m to the "left" of O