Question

suppose that a ball is rolling down a ramp. the distance traveled by the ball is given by the function s(t)=9t², where t is the time, in seconds, after the ball is released, and s(t) is measured in feet. find the balls average velocity in each of the following time intervals.
a. t₁ = 4 to t₂ = 5
\frac{delta s}{delta t}=square ft/sec

Explanation:

Step1: Find distance at $t_1 = 4$

Substitute $t = 4$ into $s(t)=9t^{2}$. So, $s(4)=9\times4^{2}=9\times16 = 144$ feet.

Step2: Find distance at $t_2 = 5$

Substitute $t = 5$ into $s(t)=9t^{2}$. So, $s(5)=9\times5^{2}=9\times25 = 225$ feet.

Step3: Calculate $\Delta s$ and $\Delta t$

$\Delta s=s(5)-s(4)=225 - 144=81$ feet, $\Delta t=t_2 - t_1=5 - 4 = 1$ second.

Step4: Calculate average - velocity

The average velocity $\frac{\Delta s}{\Delta t}=\frac{81}{1}=81$ ft/sec.

Answer:

81