Mechanics displacement Question

AI Thread Summary
The drag racer starts from rest with a velocity described by v = 5t^2. To find the displacement, integration of the velocity function is necessary. The correct expression for displacement from t = 0 to time t is derived through integration, leading to the result of 5t^3/3. Despite some confusion, the manual confirms this answer as option (b). Understanding the integration process is essential for solving similar problems in mechanics.
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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
 
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u have to apply integration here
 
Oh... I am not versed in calculus at all :l. could you explain the process?
 
express v as ds/dt. then bring the dt to other side of the equation. then integrate both sides.
 
Alright, thanks for your help!
 
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