Fi nd the displa cem ent an d the distance tr veleo ity th par ticle during the time Prob 9. A particle mo ves along a line with velocity function v(t)=t^2-t(m/s) inte rval tin [0,2]

1. Displacement is the net change in position of a particle over a time interval. For the given velocity function \(v(t) = t^2 - t\), the displacement over the interval \(t \in [0,2]\) is the integral of the velocity function from 0 to 2, which is \(\frac{2}{3}\) m. 2. Distance traveled is the total length of the path taken by the particle, regardless of direction. For the given velocity function, the distance traveled over the interval \(t \in [0,2]\) is also \(\frac{2}{3}\) m, as the particle does not change direction within this interval.