Question

Suppose a vehicle begins at rest at t=0 and accelerates at a rate given by the equation a(t) = (15 m/s^) t . Assume nonuniform acceleration.

Find the velocity a 3 seconds.

Find the displacement at 3 seconds.

Must show work.

Answer 1

See below

Step-by-step explanation:

Since it is non-uniform acceleration ( it varies with time as given)

The integral of acceleration is velocity

so integrate between 0 and three 15 m/s^2 t

= 1/2 ( 15 t^2 ) + k between 0 and 3 ( k is a constant we will ignore)

= 67.5 - 0 = 67.5 m/s velocity

the integral of velocity is displacement

1/2 (15t^2 ) integrated becomes 1/6 15 t^3 from 0 to 3 ( ignoring a constant again)

1/6 * 15 * (3^3 ) = 67.5 meters displacement

THANX for those who noted my errors in my first posted response !!