The velocity v of a particle in a time to is given by the equation v=10+2t^2 . Find the instantaneous acceleration after 5seconds

Answer 1

To find the instantaneous acceleration, we need to take the derivative of the velocity equation with respect to time.

Taking the derivative of v=10+2t^2 with respect to time t, we get:

a = d/dt(10+2t^2)
= 0 + 4t
= 4t

To find the instantaneous acceleration after 5 seconds, we substitute t=5 into the acceleration equation:

a = 4(5)
= 20

Therefore, the instantaneous acceleration after 5 seconds is 20 m/s^2.