Physics question (acceleration)

From my high school physics days I remember some basic rules having something to do with an object at rest can accelerate to a constant speed however it can not go from being at rest to a constant speed. For example a stopped car can accelerate to 60mph but it has to hit all speeds in between (at some time it will be going 25mph). Point being it can’t suddenly be at a constant 60mph from a state of rest.

My question is if i’m driving at 60mph and a stationary bug hits my windshield and suddenly is traveling along with me going 60, at what point was he going 25mph? If his acceleration started as soon as he hit my winshield wouldn’t my car in esscence have to had instantaneously dropped to zero and accelerate back to 60 with the bug in a blink of an eye?
While I was traveling at a constant 60 did I really hit 25mph along with the bug?


The collision is elastic, the bug deforms to the windshield through time (a very small time, but time nonetheless) and its center of mass speeds up very very quickly.

Look up Impact and Impulse.

The center of mass of the bug decelarates to 0, in relation to the car, then back to 60 in a very short time. The car decelarates fro 60 to 59.9999999999999999999999 and back to 60 over the same period.

A “blink of an eye” as you put it may be rather speedy on a human scale but it is a very long acceleration period when compared to the instantanious acceleration experienced by massless particles which go from 0 to c in 0 time.

While I was traveling at a constant 60 did I really hit 25mph along with the bug?

No. But the bug did. Or at least different bits of the bug at slightly different times.

Imaging the bug being at 0 mph relative to you. Then you hit it at 60 mph. The bug experiences those velocities from 0 to 60 mph. It also experiences brief, extreme acceleration, followed by zero acceleration when it reaches a constant 60 mph.

It is the extreme acceleration that creates the force that causes severe disruption of the invertebrate’s morphology.