Question

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

Answer 1

v(2)-v(0) i believe will give us the displacement of the velocity

Answer 2

int(sqrt{1+v'} dt) should give us the distance

Answer 3

there is a way using integrals

displacement=integral{v(t)dt}
distance=integral{|v(t)dt|}