Solve Car Chase Problem: Find (Delta)t & Speed of Car B

[Karma]

Homework Statement

Consider two cars A and B, initially side by side and both at rest. at t=0 car A begins to accelerate at a constant rate Aa, which continues for a a time Ta Until it reaches a speed Va, after which time it continues traveling at the constant speed Va. At the moment Car A reaches its cruising speed Va, car B takes off after Car A, accelerating at a constant rate Ab. at T=t* car B passes Car A.



C.) Determine the amount of time, (Delta)t, elapsed from the moment car B begins to accelerate to the moment it passes car A. What is the velocity of car B at the moment it passes car A? Note: You may use dimensional analysis to check your answers.

Homework Equations

The Attempt at a Solution

On a single graph i drew a Position Time Graph ... and Also i sketched a Speed-Time Graph... Me and my Roommates Have attempted to solve this problem for many hours... What can i do with the Graphs?

 

[Karma]

On my Speed-Time Graph... the constant acceleration and constant speed of Car A will be the same distance as the constant acceleration of Car B.

 

[Karma]

lol anyone??

 

[Werg22]

Look up my thread... don't tell me...

Anyway, they want you to express it algebraically. The problem is quite simple; at Ta, car A covered 1/2Aa*Ta^2. This said, you have

1/2Aa*Ta^2 + Va*delta T = 1/2Ab*delta T^2.

It's simply a question of isolation delta T here.

 

[Karma]

Yes this was my formula as well.. but 1 question how come you don't use delta T for this first part of the equation ?

is it because in the beginning ...Ta-T0...is just Ta..? ... Ahhh I get it ...If that's right..

 

[Karma]

Werg can u help me with the 2nd part of the problem

 

[Karma]

So know that i got ... (delta)t= Aa*Ta^2/Ab ...
To find the velocity when Car b passes Car A... i used the equation ...
X(final)-X(initial)=((Vxi+Vxf)/2) * t
Xf-0= ((0+Vxf)/2) *t
Xf= Vxf/2 *t
2Xf=Vxf *t
2Xf/t = VxF

so i just sub My delta T in this equation?