Question

Given an object in a straight line with a(t)=√t ft/sec^2 and v(0)=-18 for t=0 to t=16, find v(t) and the displacement and distance of the object.

Answer 1

this sounds like an integration problem

Answer 2

It is

Answer 3

What's the thought process of the problem?

Answer 4

velocity is \( \frac{dx}{dt} \) change in distance over change in time
acceleration is \( \frac{dv}{dt} = \frac{d^2x}{dt^2} \) the second derivative of x with respect to time

\[v= \int\limits_{0}^{16} \frac{dv}{dt} dt= \int\limits_{0}^{16} t^{\frac{1}{2}} dt\]