- #1

DustyGeneral

- 10

- 0

A car accelerates, starting from rest, with a speed that is given by:

v(t)=v

_{m}(1-e

^{-at})

a) What is the top speed of the car? Explain why.

b) How far does the car travel in time t?

c) Suppose the car can accelerate from 0 to 60 mph in 2.9s, and has a top speed of 195 mph. Imagine a mile-long race between two of these cars, with the same finish line, but with a different starting line: One drives along the ground towards the starting line at a point one-mile away, while the other is dropped out of a plane one mile above the ground. Which one reaches the finish line first? (ignore any air resistance for the falling car).

That is the entire problem. I just need help getting started.

First, what does the v

_{m}represent in the speed equation?

Second, how exactly do I calculate the top speed?

I also suppose that I will need the position and acceleration equations which I derived from speed equation for b and c respectively.

I got:

x(t)=v

_{m}*((e

^{-at})/a+t)

v(t)=v

_{m}*(1-e

^{-at})

a(t)=v

_{m}*(ae

^{-at})