If a car fell 4.9m over horizontal distance of 24m, was the car speeding?

There are two formulas that you want:

1) y = Voy t + 1/2g t^2

2) x = Vox t

In this case the car begins by travelling horizontally, so Voy is 0. From this we can calculate the time it takes for the car to fall.

y = 1/2gt^2

t = sqrt(2y/g) (y in this case is 4.9m)

Now we can sub that into the other equation and solve for the car's initial speed:

x = Vox * sqrt (2y/g)

Vox = x * sqrt (g/2y) (x is the horizontal distance, 24 m)

Vox = 24 * sqrt (9.8/ (2*4.9))

Vox = 24 m/s

So this car was going the speed limit, i.e. not speeding.

You can find out if the car was speeding. The gravitational constant on earth is around 9.8 m/s^2. You use the formula : d = g/2 x t^2 to find the time it was falling for, which is the same time it was going horizontally for 24 meters. You use the formula u = x / t to find the speed. That is the speed it was travelling with. Here's the math :

d = g/2 x t^2 => t = sqrt (2d/g) = sqrt(9.8/9.8) = 1 second (it was falling for 1 second)

So, since it covered 24 meters in one second, the speed was :

u = x/t = 24/1 = 24 m/s

So it was travelling EXACTLY on the speed limit. Quite easy though...

55 mph = 24.587 m/s

4.9/1/2g = t^2

g = 9.8 m/s^2 (gravity)

4.9/4.9 = 1, sq-root = 1

24/1 = 24 m/s

the car was not speeding but doing 24 m/s or 53.687 mph

Edited:

There are 1609.34 m in 1 mile, 55 x 1609.34 = 88513.7 m

88513.7/3600 secs (1 hour) = 24.587 m/s