Calc word problem! Distance and velocity with integrals.

Question

 

A particle is released. Its speed t seconds after release is given by v(t)=0.3t^2+8t. How far does the particle travel during the first 4 seconds? How far does the particle travel during the second 4 seconds.

Answer 1

Distance travelled = ∫ (0.3t² + 8t)dt   Integrate from t = 0 to 4

 

Distance travelled = 0.3t³/3   + 8t²/2

 

Distance travelled = (0.3 x 4³/3   + 8 x 4²/2) - 0

Distance travelled = 70.4 units

:)