Question

The velocity function (in meters per second) for a particle moving along a line is given by v(t) = t³ - 15t². Find the displacement and the distance traveled by the particle during the time interval [-1,7].

Answer 1

Total displacement will be 1120 meters.

Step-by-step explanation:

To calculate displacement from the velocity, need to take integral of velocity for a one time period.

`x=\int\limits^7_(-1) {t^3-15*t^2} \, dt\\x=\int\limits^7_(-1) {t^3} \, dt-\int\limits^7_(-1) {15*t^2} \, dt\\x=600-1720\\x=-1120`

The total displacement is 1120 meter in negative way.