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

Answer:

Total displacement will be 1120 meters.

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.