Kinematics - Find velocity of the car

[harrylee]

Homework Statement

Find velocity of car A when car A and car B meet
Find the distance from where car B started to where car B meets car A
Find the time it takes car A to reach car B

initial velocity of car A is 0
initial velocity of car B is 26.67 m/s
at t=5, acceleration of car B = -1/6 * acceleration of car A
velocity of car A=velocity of car B when they meet

Homework Equations

X_A(t)=X_A(0) + V_A(0)*t + .5*a_A*t^2
V_B=V_B(0) + a_B*t

The Attempt at a Solution

distance of car A equation becomes this...90=.5*a_A*t^2
velocity of car B becomes this...V_B=-26.67 - 1/6*a_A*t

I tried solving X_A equation for a_A and using it in V_B but no luck, I spent 3 days trying every which way I could think of to find the answer.

The answers in the back of the book are
Acceleration of car A=3.59 m/s^2
time=7.08 s
distance car B travels=188 m

 

[Gokul43201]

#1. Write down the time taken for A, using the least number of unknowns (use as much of the given data as possible).

#2. Write down the final speed of A in a similar manner. This is also the final speed of B.

#3. Independently, write down an expression for the final speed of B in terms of the time taken (B takes the same time as A; see #1).

#4. Use the relationship between the two accelerations and set the two expressions for the final speed of B equal to each other.