Question

The acceleration of a particle is a(t) = 60t − 4t3 m/s2. Compute the average acceleration and the average speed over the time interval [3, 7], assuming that the particle's initial velocity is zero. (Round your answers to two decimal places.)

Answer 1

Step-by-step explanation:

Acceleration function is given by

a(t) = 60 t - 4t³

To calculate the average acceleration [3,7] , use the following formula

`a_(avg)=(1)/(7-3)\int_(3)^(7)\left ( 60t-4t^(3) \right )dt`

`a_(avg)=(1)/(4)*\left ( 30t^(2)-t^(4) \right )_(3)^(7)`

Average acceleration = - 280 m/s²

velocity function is given by

`v(t) = \int a(t)dt`

`v(t) = 30t^(2)-t^(4)`

`v_(avg) = (1)/(7-3)\int_(3)^(7)\left ( 30t^(2)-t^(4) \right )dt`

`v_(avg) = (1)/(4)\left ( 10t^(3)-(t^5)/(5) \right )_(3)^(7)`

Average velocity = - 38.2 m/s