physics question?

Question

A particle moves along a line with velocity function v(t) = t2 − t, where v is measured
in meters per second. Find the displacement traveled by the particle during the time
interval [0, 4].

Answer 1

Velocity, v(t), is the derivative of the displacement.

Call displacement at time the function s(t)

ds(t)/dt = v(t)

ds(t) = v(t)dt

4...........4
∫ds(t) = ∫(t² - t)dt
0...........0

s(4) - s(0) = 4³/3 - 4²/2

s(4) - s(0) = 64/3 - 16/2 = 128/6 - 48/6 = 80/6 = 40/3

Answer 2

v = t ² - t
s = t ³ / 3 - t ²/2 between 0 and 4
s = 64/3 - 16 /2
s = 128/6 - 48/6
s = 80/6 m
s = 40/3 m