Question

Suppose an automobile was accelerating at 2 mi/h every 5 s and could keep accelerating for 2 min at that rate. How fast would it be going at `t = 12 min`? How far would it be from the starting line?

Answer 1

The final speed was `48 (mi)/(hr)` and the total distance is `8.8 mi`.

Explanation:

That acceleration would be `a = 2 ((mi)/(hr))/(5 s) = 0.4 ((mi)/(hr))/s`. I will assume the acceleration after 2 minutes was zero. Converting the 2 minute time to 120 s and using the kinematic formula

`v = u + a*t`

`v = 0 + 0.4 ((mi)/(hr))/s* 120 s = 48 (mi)/(hr)`

To find the distance traveled during that 2 minute acceleration, we can calculate average speed since the acceleration was constant for the 2 minutes.

`s = (u + v)/2 * t = 48/2 (mi)/cancel(hr) * 2 cancel("minutes") * (1 cancel(hour))/(60 cancel("minutes")) = 0.8 "miles"`

At a constant speed of 48 (mi)/(hr), 10 more minutes of driving will increase the distance by

`48 (mi)/cancel(hr) * 10 cancel("minutes") * (1 cancel(hour))/(60 cancel("minutes")) = 8 "miles"`

So the total distance is 8.8 miles.

I hope this helps,
Steve