Question

1a. You are driving down the street at a constant speed of 60mph. Draw a graph of distance versus time over the course of 4 hours.

b. How would you use the graph to determine the rate (speed in mph) at which the car is traveling (assuming you did not already know the answer)? Hint: What is the slope for the graph in part A? What does the term slope mean?

c. Now draw a new graph (still distance vs. time). Assume that at t=1 hour you removed your foot from the accelerator, and that the car coasts to a stop after 1 hour. (We know that is not realistic, just think about the shape of the curve.)

d. Does the car move at a constant rate (speed) as it is slowing down? Why or why not?

e. Why do the two graphs look different? (hint: they should look different!)

f. In the time between t=1 and t=2, how would you estimate your speed (using the second graph you drew)? (Why do we need to specify the time?)

g. If you wanted to know your speed at 1.5 hours after you started how would you estimate it by using the graph? (sketch your answer below)

Answer 1

1.a
Let s= Distance for any time t
s = 60mph * t (in h) = 60 t
s = 60t

η |

b. speed is in mph that is 60/1 = 60mph or 120/2=60mph and so on, from the graph, it is the slope of the line (distance-time graph)

c.

d.

Yes because the slope is same as speed from 60mph(at t= 1hour) decreases to 0mph at t = 2 hour

e.

They are different because on first case the car goes on and on whereas in the second case it comes to a halt after 2 hours.

f.
Speed can be estimated by the slope of the distance-time graph.

g

The slope of the graph at t =1.5 h gives us the speed.