If 100mph Car Crashes into a car doing 60 mph...?

Question

If a car speeding at 100mph on a highway crashes into the rear end of a car traveling at 60mph, would the impact be the same (or greater) as a car at 40 crashing into a stationary car? What does physics have to say about the difference? Thanks to all in advance for indulging me.

Answer 1

Let's see if it's the same or not using some equations of momentum and energy
100 mph = 44.70400 meters / second
60 mph = 26.8224 meters / second
40 mph = 17.8816 meters / second

Let's assume the cars have equal mass and stick together after the collision

case 1

44.7*m+26.822*m=v*2*m
v=35.761 m/s
The change in kinetic energy is
.5*m*44.7^2+.5*m*26.822^2-m*35.761^2
79.9 J

case 2
17.88*m=v*2*m
v=8.94 m/s
The change in energy is
.5*m*17.88^2-m*8.94^2
79.9 J

The loss of energy is the same.

And the acceleration is the same

j

Answer 2

Either way you are crashing into something at 40mph so the impact is the same.

If you consider the frame of reference to be the car that is going to be hit, then either way that car is stationary while it is hit at 40mph, so the impact is the same.

Answer 3

As far as physics questions are concerned they are the same