Question

the velocity function, in meters per second, of a particle moving is given by v(t)=5t-2where t is time in seconds. Find the displacement of the particle from t=0 seconds to t=6 seconds

Answer 1

Remember that displacement is the integral of the velocity, so you have o integrate the velocity function between 0 and 6 seconds to find the displacement in the first 6 seconds.

$\int _0^65t-2dt$$d(t)=\frac{5t^2}{2}-2t$$d(6)=\frac{5(6)^2}{2}-2(6)=90-12=78$$d(0)=0$$78-0=78$

So the displacement in the first 6 seconds is 78 meters.