When does Kathy overtake Stan in the drag race?

[jp0108]

Homework Statement

A young woman named Kathy Kool buys a
sports car that can accelerate at the rate of
4.56 m/s2. She decides to test the car by drag
racing with another speedster, Stan Speedy.
Both start from rest, but experienced Stan
leaves the starting line 0.51 s before Kathy.
Stan moves with a constant acceleration of
3.43 m/s2 and Kathy maintains an accelera-
tion of 4.56 m/s2.
Find the time it takes Kathy to overtake
Stan. Answer in units of s.

The formulas are:

vf = vi + at

d = vit + 1/2at^2

vf^2 = vi^2 + 2ad

d = 1/2 (vi + vf) delta t

a = delta v/ t

v = d/t


KEY:
v: m/s
d: m
t: s
a: m/s^2
vi: initial velocity
vf: finial velocity
delta v: change in velocity

 

[berkeman]

Homework Statement

A young woman named Kathy Kool buys a
sports car that can accelerate at the rate of
4.56 m/s2. She decides to test the car by drag
racing with another speedster, Stan Speedy.
Both start from rest, but experienced Stan
leaves the starting line 0.51 s before Kathy.
Stan moves with a constant acceleration of
3.43 m/s2 and Kathy maintains an accelera-
tion of 4.56 m/s2.
Find the time it takes Kathy to overtake
Stan. Answer in units of s.

You need to show us the relevant equations, and show us your attempt at a solution before we can help you. That's the PF Rules (see the link at the top of the page).

 

[jp0108]

the formulas are:

vf = vi + at

d = vit + 1/2at^2

vf^2 = vi^2 + 2ad

d = 1/2 (vi + vf) delta t

a = delta v/ t

v = d/t


KEy:
v: m/s
d: m
t: s
a: m/s^2
vi: initial velocity
vf: finial velocity
delta v: change in velocity

 

[berkeman]

d = vit + 1/2at^2

This would be the most useful equation of the bunch for this problem. Why?

Now write the two equations for the d(t) of the two cars, including the initial conditions you've been given, and find at what time t the two d(t) numbers are equal...