How Far and Fast Does Tina Drive to Pass David?

[mullets1200]

Homework Statement

David is driving at a steady 26.0m/s when he passes Tina who is sitting in her car at rest. Tina begins to accelerate at a stead 2.20 m/s² at the instant when david passes.

Questions to answer:
1) How far does Tina drive before passing David?

2)What is her speed as she passes him?

 

[diazona]

What about the rest of the question template? What have you tried? What do you know that is relevant to this problem?

 

[kerimek]

I would approach this problem by using the basic formula for acceleration, which is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. In this case, we are given the initial velocity of David (vi = 26.0m/s) and the acceleration of Tina (a = 2.20 m/s^2). We are also given that Tina starts accelerating at the instant when David passes her, so we can assume that their time is the same.

1) To answer the first question, we need to find the time it takes for Tina to catch up to David. We can do this by setting their final velocities equal to each other, since they will have the same final velocity when she passes him. So, we have 26.0m/s = 2.20m/s^2*t. Solving for t, we get t = 11.82 seconds. Now, we can use the formula d = vi*t + 1/2*a*t^2 to find the distance Tina travels before passing David. Plugging in the values, we get d = 26.0m/s * 11.82s + 1/2 * 2.20m/s^2 * (11.82s)^2 = 155.2m. Therefore, Tina will drive 155.2m before passing David.

2) To answer the second question, we can use the formula vf = vi + a*t to find Tina's final velocity when she passes David. Plugging in the values, we get vf = 26.0m/s + 2.20m/s^2 * 11.82s = 51.6m/s. So, Tina's speed as she passes David will be 51.6m/s.

In conclusion, using the basic formula for acceleration and understanding the given information, we can calculate the distance Tina drives before passing David and her speed at that moment. This problem showcases the relationship between velocity, acceleration, time, and distance, which are fundamental concepts in the study of motion.