Question

David is driving at a steady 30.0 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.70 m/s^2 at the instant David passes. How far does Tina drive before passing David and what is her speed as she passes him?

Answer 1

Let t=0 when David passes Tina.
Consider the speed of Tina.
v0=0 m/s
a=2.7 m/s²
Assuming Tina accelerates indefinitely, at time t when she overtakes David, they would have travelled the same distance since t=0.
Distance travelled by David
= 30t
Distance travelled by Tina
=v0*t + (1/2)at²
Equate and solve for t.
Her speed would be a*t.

Answer 2

690 m