Question

The formula d = t² + 5 t expresses a car's distance (in feet) from a stop sign, d, in terms of the number of seconds t since it started moving.

Determine the car's average speed over the interval of time from t = 4 seconds to t = 7 seconds.

Answer 1

The car's average speed is 16 feet per second.

Step-by-step explanation:

The expression for the average speed is as follows;

`A.S=\frac{\textrm{Total distance}}{\textrm{total time}}`

Given expression of distance:

`d=t^(2)+5t`

Put t= 4 s.

`d(4)=(4)^(2)+5(4)`

d(4)= 36 ft

Put t= 7 s in the given expression.

`d(7)=(7)^(2)+5(7)`

d(7)= 84 ft

Calculate the car's average speed over the interval of time from t = 4 seconds to t = 7 seconds.

`A.S=(d(7)-d(4))/(7-4)`

`A.S=(84-36)/(7-4)`

A.S= 16 feet per second

Therefore, the car's average speed is 16 feet per second.