Question

Three cars start traveling at the same time. The distance traveled by each is represented in three different ways, with y representing miles traveled and t representing time passed in hours.

Use the images to answer the question.

Car 1:

y=t

Car 2:

Distance Traveled by Car 2 at Different Time Intervals


0

0.2

0.4

0.6

0.8

1



0

0.04

0.16

0.36

0.64

1

Car 3:

A coordinate plane goes from negative 5 to 5 on the t-axis in intervals of 1 and from negative 5 to 5 on the y-axis in intervals of 1.
▶Click for Long Desc

Compare the speeds of the 3 cars after 5 hours. In your answer, describe the function represented by each car.

(2 points)

Math Short Answer Rubric (2 points)

Answer 1

I can’t see the Car 3 graph clearly from your description. I can do the full comparison once you either (a) paste or describe the Car 3 graph (e.g. give two points on it or its equation), or (b) tell me the rule for Car 3.

What I can say now from the given info:

- Car 1: y = t. This is a linear function with constant speed 1 mile per hour. After 5 hours it has gone 5 miles.

- Car 2: the table (0 → 0, 0.2 → 0.04, 0.4 → 0.16, 0.6 → 0.36, 0.8 → 0.64, 1 → 1) matches y = t^2. This is a quadratic (distance grows faster over time); its instantaneous speed is dy/dt = 2t, so at t = 5 hours the speed is 10 mph and the distance is y = 25 miles.

If the Car 3 graph is a line through the origin with slope m, then Car 3’s function is y = m t (constant speed m mph) and its distance after 5 hours is 5m miles. For example, if the graph is y = 3t then after 5 hours Car 3 has gone 15 miles, so the ranking would be: Car 2 (fastest), Car 3 (middle), Car 1 (slowest).

Send the Car 3 graph description (two points or the equation) and I’ll finish the comparison precisely.