How to find the speed of a passing car

Question

Can someone check my work on this problem?

I'd like to be able to figure out how fast cars are going by measure the time it takes to pass me, or for me to pass them. I figure, counting the seconds it takes for one car to pass the other will give me the relative velocity and then I can just add or subtract that from my velocity (assuming all speeds are constant). Here are my calculations:

Say 1 car length = 13.5 ft

Call the number of seconds it takes for the car to pass me $x$

Then their relative speed is $\frac{13.5 \ ft}{x \ sec} (\frac{1 mi}{5280 ft})(\frac{60 \ sec}{1 \ hr}) = \frac{.1534}{x}$mph.

Now suppose my speed is y mph. Then their "absolute speed" is (y + $\frac{.1534}{x}$)mph.

Are my calculations correct? Something seems wrong here.

Answer 1

There are 3600 seconds in an hour, not 60. You should get $y + \frac{9.20455}{x}\mathrm{ mph}$

Answer 2

Starting from $v=d/t$, given the same distance traveled, $$v_1*t_1=v_2*t_2,$$ or $$v_2=v_1*(t_1/t_2).$$

The speed of a passing car (2) is equal to the speed of your car (1) multiplied by the time your car takes to travel a set distance compared to the time it takes the other car to travel the sane distance. The procedure is as follows: you see a car in your rear-view mirror approaching to pass you. Maintain a constant speed and wait for the front of the other car to be even with yours. At that instant, begin counting steadily 0, 1, 2, until 10. When reaching a count of 10, identify a marker on the road near the front end of the other car. The marker can be a light post, a traffic lane marker, a stain on the road, or anything static. Keep counting at the same pace past 10 until the front of your car crosses that marker.

Don’t stop or change the pace as you count past 10 until you reach the marker. At that point your car has traveled the same distance than the other car did in 10 counts. Now the formula for $v_2$ can be applied to find the other car’s speed. For example, if your car is traveling at 70 mph and the time it took for your car to reach the other car’s 10-count marker was 14 counts, then the other car’s speed is $$v_2 = 70*14/10 = 98$$. A simplified way to calculate this is $$70 + 4*7 = 70 + 28 = 98$$ mph. This method estimates the other car’s average speed within the 10 counts. The other car may be traveling at a constant speed or variable speed, the formula still applies as long as your speed is kept constant. It also works regardless of how fast or slow you count, as long as you count at a constant rate.