Dealing with Velocity and acceleration. What do I do next? =P

[CowzRule101]

Homework Statement

David is driving a steady 21.0 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 when David passes.

David:
V= 21m/s

Tina:
V_i= 0 m/s
V_f= ?
acc= 2.7 m/s^2

How far does Tina drive before passing David?
What is her speed as she passes him?

Homework Equations

D_f= D_i + V_i + t_f + (1/2)at_f^2
V_f^2= V_i^2 + 2a(D_f - D_i)
V_f= V_i +at

The Attempt at a Solution

Well, I really don't have an attempt because I have no clue what to do. Any suggestions

 

[Kurdt]

At the point Tina catches David their distances should be the same. You can set the two equations of motion equal and then solve for time. Once you have time you can solve for the other things.

 

[baba89]

?


Hi there! It looks like you are dealing with some basic kinematics problems involving velocity and acceleration. To help you figure out what to do next, let's break down the problem step by step:

1. Identify what is given and what is asked for: In this problem, we are given the initial velocity of David (21 m/s), the acceleration of Tina (2.7 m/s^2), and the initial velocity of Tina (0 m/s). We are asked to find the distance Tina drives before passing David and her speed as she passes him.

2. Choose an appropriate equation to use: From the equations you have listed, it seems like the most appropriate one to use in this case is V_f^2= V_i^2 + 2a(D_f - D_i), since we know the initial and final velocities of Tina and the acceleration she experiences.

3. Plug in the given values: Substitute the values you know into the equation. In this case, we have V_i=0 m/s, V_f=?, a=2.7 m/s^2, and D_i=0 m. We are trying to solve for D_f, the distance Tina drives before passing David.

4. Solve for the unknown variable: Now that we have plugged in all the known values, we can solve for the unknown variable, which in this case is D_f. This will give us the distance Tina drives before passing David.

5. Calculate Tina's speed as she passes David: To find Tina's speed as she passes David, we can use the equation V_f= V_i +at, since we know her initial velocity and acceleration. Plug in the values and solve for V_f.

6. Double check your answer: Always make sure to double check your answer and make sure it makes sense in the context of the problem. In this case, the distance Tina drives should be greater than 21 m (since she is accelerating) and her speed should be greater than 21 m/s (since she is catching up to David).

I hope this helps guide you in the right direction for solving this problem. Remember to always identify what is given, what is asked for, and choose an appropriate equation to use. Good luck!