Question

Solve for velocity at 6 seconds

The figure below gives the acceleration a versus time t for a particle moving along an x axis. At t--2.0 s, the particle's velocity is-35 m/s, what is its velocity at t-6.0 s? -105 X m/s a (m/s2) t (s)

Answer 1

a = - 7.5/4*t+7.5

a=-1.875t+7.5

dv/dt =-1. 875t + 7.5

dv =(-1.875t + 7.5)dt

Integrating it

V= - 1.875t^2/2+7.5t +V0

t=-2sec, v=-35m/sec

-35 = - 1.875*(-2)^2/2+7.5*(-2)+V0

V0=-20+3.75=-16.25

At t=6sec

V= - 33.75-45-16.25=-95 m/sec