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 2.90m/s2 at the instant when David passes.

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To answer this question, we need to find out how much time it takes for Tina to catch up to David.

We can start by calculating the distance David travels during this time. The formula to calculate distance is:

distance = speed × time

Here, David's speed is given as 24.0 m/s. So, to find the distance David travels, we need to know the time it takes for Tina to catch up to him.

Let's assume that Tina catches up to David after time 't'. During this time, David travels a distance 'd'.

Now, we can use Tina's information to calculate her distance using the following formula:

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

Since Tina is initially at rest, her initial velocity is 0 m/s. Her acceleration, given as 2.90 m/s^2, should be positive because she is accelerating to catch up with David. We can substitute the values into the formula and solve for the distance:

d = 0 × t + (1/2) × 2.90 × t^2
d = (1.45) × t^2

Now, let's set this distance equal to the distance traveled by David:

(1.45) × t^2 = 24.0 × t

Now, let's solve this equation for 't'. To do so, we can divide both sides of the equation by 't':

(1.45) × t = 24.0

Next, let's isolate 't' by dividing both sides by 1.45:

t = 24.0 / 1.45

By calculating this equation, we find that:

t ≈ 16.55 s

Therefore, it takes Tina approximately 16.55 seconds to catch up to David.