A particle moves along the x axis with velocity of v(t) m/s. Find the displacement and distance travelled

over the given time interval for:

a) v(t) = 3t-2 for 0 ≤ t ≤ 2
b) v(t) = |1-2t| for 0 ≤ t ≤ 2

Displacement is distance traveled in one direction (in case you didn't know)

You need to integrate from velocity to get an equation for displacement

the integral of a) is [1.5t^2 - 2t] between 2 and 0
therefore, [1.5(2^2) - 2(2)] - [0]
therefore = 2metres

the integral of b) is [t - t^2] between 2 and 0
therefore [2 - (2^2)] - [0 - 0^2]
therefore = I-2I metres
therefore = 2metres.