Question

Ben is spending his summer driving across the country. He is going to spend the first day just driving straight west. The table below shows the distance traveled as a function of time.

Distance 55 110 165 220 275 330
time 1 2 3 4 5 6
a. Graph this relationship on a coordinate plane.
b. Find the slope of the line.
c. What information about Ben’s speed can you obtain from the slope?
d. Write an equation to represent the distance traveled after driving a given number of hours. Label each variable.

Answer 1

(a) The distance vs time graph of Ben's motion is in the image attached.

(b) The slope of the line of distance vs time graph is 55 m/s.

(c) Based on the slope calculated, Ben is driving at a constant speed throughout his journey.

(d) The equation representing the distance traveled by Ben after given number of hours is y = 55x + 10

How to graph the distance time graph?

(a) The distance vs time graph of Ben's motion is graphed by plotting the distance on y - axis and time of motion on x - axis.

(b) The slope of the line of distance vs time graph is calculated as;

m = Δy/Δx

m = (330 - 55) / (6 - 1)

m = 55 m/s

(c) Based on the slope calculated, we can deduce that Ben is driving at a constant speed throughout his journey.

(d) The equation representing the distance traveled by Ben after given number of hours is calculated as;

y = mx + c

where;

• m is the slope of the line
• c is the y intercept of the line

from the graph, the y - intercept is approximately 10 m

y = 55x + 10