Question

Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s (t )equals 3 t squared​, where t is the​ time, in​ seconds, after the ball is​ released, and​ s(t) is measured in feet. Find the​ ball's average velocity in each of the following time intervals.

Answer 1

Answer:$v_{avg}=\frac{3\left ( t_2^2-t_1^2\right )}{t_2-t_1}$

Step-by-step explanation:

Given

Distance traveled is function of time

$s(t)=3t^2$

ball average velocity from time $t=t_1 to\ t=t_2$

distance traveled in $t=t_1 s$

$s(t_1)=3t_1^2$

Now Distance traveled in $t=t_2 s$

$s(t_2)=3t_2^2$

Distance traveled between $t=t_1 to t=t_2$

$\Delta s=3\left ( t_2^2-t_1^2\right )$

$\Delta t=t_2-t_1$

Average velocity$=\frac{\Delta s}{\Delta t}$

$v_{avg}=\frac{3\left ( t_2^2-t_1^2\right )}{t_2-t_1}$