Question

A particle travels along the x-axis such that its velocity is given by v(t) = (t^0.7 + 4t) cos (t^2). What is the average acceleration of the particle on the interval 0thousandth.

Answer 1

It's not clear to me what the given interval is supposed to be, so I'll use a generic one, [a, b] with a < b.

The average acceleration of the particle over this interval is given by the average rate of change of v(t),

$a_{\rm ave} = \dfrac{v(b) - v(a)}{b - a} = \boxed{\dfrac{(b^{0.7}+4b)\cos(b^2) - (a^{0.7}+4a)\cos(a^2)}{b - a}}$