Question

Adam is driving a steady 35 m/s when he passes Sarah, who is sitting in her car at rest. Sarah begins to accelerate at a steady 3.0 m/s^2 at the instant when Adam passes. How far does Sarah drive before passing Adam ?

Answer 1

Adam's Initial Velocity = 35 m/s
Sarah's Initial Velocity = 0 m/s

Sarah's Acceleration = 3m/s^2

You need to begin with:
\[V _{f} Adam = V _{f} Sarah\]

Answer 2

What is V final of Sarah?

Answer 3

so that is the just the integral of second derivative of the position function, right?

Answer 4

Wait sorry, we're taking this one step at a time.
Vf Adam = 35m/s because he's not accelerating.

First you need to find how long it takes for Sarah to catch up to Adam's speed.

You do this by setting
V Adam = VSarah
35 = 3t
t = 4 seconds, it takes Sarah 4 seconds to get to 35 m/s.

Answer 5

Also I'm taking trig-based Physics not Calc-based. But we'll get the same answer.

Answer 6

I think I get it, thanks!

Answer 7

You're welcome:)

Answer 8

Sorry, idk how i got 4 secs.... 35/3 is 11.666667 sec.

Answer 9

But yeah.

Answer 10

That's fine, you made it clear to me when you put v=v. That's want I needed. Thanks again.