a particle moves in a straight line so that t seconds after passing a fixed point O its acceleration a cm per second is given by a=4t-16. It passes O with a velocity of 30cm per second.

Question

Find an expression for the velocity of the psrticle in terms of t and show that it comes to instantenous rest when t=3

Answer 1

a = 4t - 16
integrating ...
v = 2t^2 - 16t + c
given: at t=0, v = 30
30 = 0-0+c
c = 0

velocity = 2t^2 - 16t + 30
when t=3
velocity = 2(9) - 16(3) + 30 = 0
looks like it is resting.