A car is driving away from a crosswalk. The formula d = t 2 + 2 t expresses the car's distance from the crosswalk in feet, d , in terms of the number of seconds, t , since the car started moving.

Question

A car is driving away from a crosswalk. The formula  expresses the car's distance from the crosswalk in feet, , in terms of the number of seconds, , since the car started moving.

Suppose  varies from to 

What is the car's average speed over this interval of time?

Suppose  varies from  to .

1. 
   
2. 
   
3. What is the car's average speed over this interval of time?

Answer 1

The formula for average speed is: change in distance ÷ change in time

Since the formula for distance is given -- d = t² + 2t -- we can substitute the given time values for t.

t = 1 to t = 5

d(1) = 1² + 2(1) = 3ft

d(5) = 5² + 2(5) = 35ft

So, the average speed for this interval of time would be

35 - 3 32

––––– = ––– = 8 ft/s

5 - 1 4

The same formula is used for the second part of the question only using values d(1.4) and d(2.2).

d(1.4) = 1.4² + 2(1.4) = 4.76ft

d(2.2) = 2.2² + 2(2.2) = 9.24ft

9.24 - 4.76 4.48

————— = ——— = 5.6 ft/s

2.2 - 1.4 0.8