Thread: Acceleration

A particle moves in a straight line with a constant acceleration a m/s^2. At time t=0, the particle's velocity is u m/s.

(a) Using the differential equation a=dv/dt, show that the velocity v, at time t is v=u+at.

I haven't a clue what to do although it involves integration.

Originally Posted by Stuck Man

A particle moves in a straight line with a constant acceleration a m/s^2. At time t=0, the particle's velocity is u m/s.

(a) Using the differential equation a=dv/dt, show that the velocity v, at time t is v=u+at.

I haven't a clue what to do although it involves integration.

get the equation into the form a dt = dv. now integrate both sides. you should get at + C = v since a is just a constant. the initial condition given to you says that at time t=0, v = u. so plug those in and you get a(0) + C = u or C = u.

so therefore v = u + at

I still don't understand. I haven't seen anything like this. I don't know why the book gives a question like nothing its covered before.

Are you able to differentiate

u + at

with respect to t, assuming u and a are constants?

I suppose I've understood. Thanks.