A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 19.0m/s , and the distance between them is 52.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 5.00m/s2. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2−t1

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2.5 To find the time it takes for the motorcycle to catch up with the car, we need to find t2. Here's how we can approach the problem:

1. Determine the initial velocity of the motorcycle: Since the motorcycle and the car are initially traveling at the same speed, the initial velocity of the motorcycle is also 19.0 m/s.

2. Calculate the displacement of the motorcycle during the time t1: The displacement can be calculated using the formula:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the motorcycle is not accelerating during the time t1, the displacement would be:
displacement = (19.0 * 5.00)

3. Calculate the relative displacement between the car and motorcycle after t1: The relative displacement is the initial distance between them minus the displacement of the motorcycle during t1. So,
relative displacement = 52.0 - displacement

4. Find the time it takes for the motorcycle to catch up with the car: The time required to catch up is the time it takes for the relative displacement to be zero. We can calculate this using the formula:
relative displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Substitute the relative displacement as zero and solve for time.

0 = (19.0 * t2) + (0.5 * (5.00) * t2^2)

This is a quadratic equation that can be solved to find t2.

5. Calculate t2 - t1: Once you find the value of t2, subtract t1 from it to get t2 - t1.

And that's how you can find t2 - t1, which represents the time it takes from the moment when the motorcycle starts to accelerate until it catches up with the car.