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)=(5t^2)/(2)-2t`
`d(6)=(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.