Question

A particle moves with a fixed acceleration of 3 m/s^2. If its initial velocity is v(0)= 2 m/s, and its initial displacement is s(0)= 0

A)Find its velocity function v(t)

B)How long does it take for the particle to reach the velocity 14 m/s?

C)Find the distance traveled when its velocity reaches 14 m/s.

Answer 1

v = 2 + 3t
when does v=14?
now take the integral to get the distance

Answer 2

Thank you so just to clarify for a) all you did was take the integral of the acceleration to get your v(t) function.

Then for b) do you set v=2+3t equal to 14?

c)You just take the integral of v(t) to get position function I think.

Answer 3

Yes.

The integral of the acceleration vector is the velocity vector. The constant of integration is determined by a known velocity, often the initial velocity.

The integral of velocity is displacement. Constant of integration is determined by initial position (zero here) to give position as a function of time.