The velocity of a particle moving along a line is v(t)= 2t^3 - t +1.

Question

The velocity of a particle moving along a line is v(t)= 2t^3 - t +1.

a) Find the total distance traveled by the particle over the time interval (2,5)

b) Find the net displacement of the particle over the time interval (2,5)

Answer 1

Because v(t) > 0 over the entire interval, displacement = total distance traveled = ∫₂⁵ v(t)dt.

∫₂⁵ v(t)dt = 1/2 t⁴ - 1/2 t² + t ]₂⁵ = 305 - 8 = 297