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

Answer:

Explanation:

Acceleration function is given by

a(t) = 60 t - 4t³

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

$a_{avg}=\frac{1}{7-3}\int_{3}^{7}\left ( 60t-4t^{3} \right )dt$

$a_{avg}=\frac{1}{4}\times\left ( 30t^{2}-t^{4} \right )_{3}^{7}$

Average acceleration = - 280 m/s²

velocity function is given by

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

$v(t) = 30t^{2}-t^{4}$

$v_{avg} = \frac{1}{7-3}\int_{3}^{7}\left ( 30t^{2}-t^{4} \right )dt$

$v_{avg} = \frac{1}{4}\left ( 10t^{3}-\frac{t^5}{5} \right )_{3}^{7}$

Average velocity = - 38.2 m/s