David is driving a steady 24.0m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.70m/s^2 at the instant when David passes.

How far does Tina drive before passing David?

What is her speed as she passes him?

distance=

(velocity)*(time)=(1/2)(acceleration)(time)^2

set the distances equal.

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My name is jeff

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To find the distance Tina drives before passing David, we need to find the time it takes for her to catch up to him.

First, let's calculate this time. We can use the equation of motion:

distance = initial velocity * time + (1/2) * acceleration * time^2

Here, the initial velocity of Tina's car is 0 m/s (as she is at rest initially), the acceleration is 2.70 m/s^2, and the distance is the unknown parameter.

Using the above equation, we can rewrite it as:

distance = (1/2) * acceleration * time^2

Rearranging the equation to solve for time:

time = sqrt((2 * distance) / acceleration)

Now, let's calculate the time it takes for Tina to catch up to David. Since we want to know the distance Tina drives before passing David, we can assume that they both travel the same distance in that time.

Using the equation of motion for David:

distance = David's speed * time

Substituting the calculated time into the equation, we have:

distance = David's speed * sqrt((2 * distance) / acceleration)

Now, we can solve for distance. Let's rearrange the equation to isolate "distance" on one side:

distance - (David's speed * sqrt((2 * distance) / acceleration)) = 0

To solve this equation, you can use numerical methods or approximation techniques. One way is to use a graphing calculator or software to plot the function and find the point where the graph intersects the x-axis. Alternatively, you can use iterative approximation techniques like the Newton-Raphson method.

Now, let's calculate Tina's speed as she passes David. Since both cars are traveling at the same time when Tina overtakes David, they will have the same time value. So, we can use the time calculated above and substitute it into Tina's equation of motion:

Tina's speed = initial velocity (0 m/s) + (acceleration * time)

Substituting the values:

Tina's speed = 2.70 m/s^2 * sqrt((2 * distance) / acceleration)

You can now calculate Tina's speed as she passes David by substituting the value of distance (found earlier) into the equation.