Mechanics displacement Question

[Kommandant]

Homework Statement

At time t = 0 a drag racer starts from rest at the origin and moves along a straight line with velocity given by v = 5t^2, where v is in m/s and t in s. The expression for the displacement of the car from t = 0 to time t is
(a) 5t^3
(b) 5t^3/3
(c) 10t
(d) 15t^2
(e) 5t/2

Homework Equations

(Vfinal-Vinitial/2)t=X
Vfinal=5t^2

The Attempt at a Solution

The manual says B

But I keep Getting 5t^3/2

Vfinal=5t^2

Vinitial=0
so
(5t^2/2)t=x
5t^3/2

 

[Swap]

u have to apply integration here

 

[Kommandant]

Oh... I am not versed in calculus at all :l. could you explain the process?

 

[Swap]

express v as ds/dt. then bring the dt to other side of the equation. then integrate both sides.

 

[Kommandant]

Alright, thanks for your help!