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.

 

[m2003]

As a scientist, it is important to always check your equations and make sure they are accurate. In this case, the equations you have used are not sufficient to find the velocity of car A or the distance and time it takes for car A and car B to meet.

To solve this problem, we can use the equations of motion in one dimension, which are:
- x = x0 + v0t + 1/2at^2
- v = v0 + at

First, we need to find the acceleration of car A. We know that at t=5, the acceleration of car B is -1/6 times the acceleration of car A. This means that at this time, the two cars are moving at the same velocity. So, we can set the two velocity equations equal to each other and solve for a:
- V_A = V_B
- 0 = 26.67 + (-1/6)a(5)
- a = 3.59 m/s^2

Now, we can use this acceleration to find the time it takes for car A to reach car B. We know that the final velocity of both cars is the same, so we can set the two velocity equations equal to each other and solve for t:
- V_A = V_B
- V_A = 26.67 + 3.59t
- t = 7.08 s

Finally, to find the distance car B travels, we can use the distance equation for car B and solve for x:
- x = x0 + v0t + 1/2at^2
- x = 0 + 26.67(7.08) + 1/2(3.59)(7.08)^2
- x = 188 m

In conclusion, the velocity of car A when it meets car B is the same as the velocity of car B, which is 26.67 m/s. The time it takes for car A to reach car B is 7.08 seconds, and the distance car B travels is 188 meters.