Question

James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed time? f = 6.2 + n n = 6.2 + f f = 6.2n n = 6.2f

Answer 1

Elapsed Time (Seconds)                   Distance Travelled (Feet)
                1                                                          6.2
                2                                                        12.4
                3                                                        18.6
                4                                                        24.8

To form an equation, we first need to check whether the changing rate is a linear or non-linear.

A linear rate would give the same changing rate every one second traveled

Distance traveled between second 1 and second 2 = 12.4 - 6.2 = 6.2
Distance traveled between second 2 and second 3 = 18.6 - 12.4 = 6.2
Distance traveled between second 3 and second 2 = 24.8 - 18.6 = 6.2

Since the increase is the same every second, 6.2 feet, our equation would be the linear equation which is in the form y = mx + c
Where 'm' represents the gradient (changing rate) and c represents the distance traveled when the time is zero, which is also zero

n = 1 ⇒ d = 6.2
n = 0 ⇒ d = 6.2 - 6.2 = 0

We have m = 6.2 and c = 0
The equation is f = 6.2n 

Answer: Option 3