Calculus Problem: acceleration, speed, and displacement of a particle

[Stephanievet54]

Homework Statement

The acceleration of a particle given a=A√t where A=2.0 m/s^5/2. At t=0, v=7.5 m/s and x=0. (a) What is the speed as a function of time? (b) What is the displacement as a function of time? (c) What are the acceleration, speed, and displacement at t=5.0s.

Homework Equations

The Attempt at a Solution

I tried to integrate a=A√t, but I don't know where to plug in v and x. Any help will be greatly appreciated.

 

[kuruman]

Hi Stephanievet54 and welcome to PF.

Can you show in detail what you tried to do? Remember that in physics you deal with definite integrals. For example, if $a=\frac{dv}{dt}$, then $$\int_{v_0}^v dv=\int_{t_0}^{t}a(t') dt'$$Note that at the lower limit of time $t_0$ the velocity is $v_0$ and at the upper limit of arbitrary time $t$ the velocity is $v$. The integration on the right is over dummy variable $t'$. Similar considerations apply for $x(t)$.