Question

A car is driving away from a crosswalk. The formula d = t2 + 2t expresses the car's distance from the crosswalk in feet, d, in terms of the number of seconds, t, since the car started moving. Suppose t varies from t=1to t=5. What is the car's average speed over this interval of time?

Answer 1

Answer:

8 feet per second.

Step-by-step explanation:

We have been given that a car is driving away from a crosswalk. The formula $d=t^2+2t$ expresses the car's distance from the crosswalk in feet, d, in terms of the number of seconds, t, since the car started moving.

We will use average change formula to solve our given problem.

$\text{Average change}=\frac{f(b)-f(a)}{b-a}$

$\text{Average change}=\frac{d(5)-d(1)}{5-1}$

$\text{Average change}=\frac{(5)^2+2(5)-((1)^2+2(1))}{4}$

$\text{Average change}=\frac{25+10-(1+2)}{4}$

$\text{Average change}=\frac{35-3}{4}\\\\\text{Average change}=\frac{32}{4}\\\\\text{Average change}=8$

Therefore, the the car's average speed over the given interval of time would be 8 feet per second.