Kinematics

[Eklav Rai]

A particle moves in a straight line, so that t s after leaving a fixed point 0,its velocity , Vm/s, is given by: v= pt²+qt+4

Where p and q are constants. When t=1 the acceleration of the particle is 8m/s. When t=2 the displacement of the particle from 0 is 22m.Find the value of p and of q.

[Open Intelligence]

acceleration = integration of velocity

a = dv/dt

a = 2pt + q

t=1, 2p + q = 8

s = integration of v

s = [pt³/3 + qt²/2 + 4t], limits 2 and 0 = 22

8/3p + 2q + 8 = 22

8p + 6q = 42

q = 5, p = 1.5