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 21.5 m/s , and the distance between them is 52.0 m . After t1 = 4.00 s , the motorcycle starts to accelerate at a rate of 5.00 m/s2 . The motorcycle catches up with the car at some time t2. 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.
A spacecraft traveling at a speed of 1200 m/s is uniformly accelerated at the rate of 150 m/s/s. If the acceleration lasts for 1.8 seconds, what is the final speed of the craft?
To find the time it takes for the motorcycle to catch up with the car, you will need to calculate the time it takes for the motorcycle to cover the initial distance and catch up to the speed of the car. Once you have this time, you can subtract t1 (4.00 s) from it to find the answer (t2 - t1).
Let's break down the problem into steps:
Step 1: Find the distance covered by the motorcycle during the acceleration phase.
To find the distance covered during acceleration, you can use the kinematic equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
The initial velocity of the motorcycle is 21.5 m/s, and the acceleration is 5.00 m/s^2. The time is t1 (4.00 s).
Plugging in the values into the equation, we get:
distance = 21.5 * 4 + (1/2) * 5 * 4^2
Simplifying the equation:
distance = 86 + 40 = 126 meters
Step 2: Find the time it takes for the motorcycle to catch up to the car's speed.
The motorcycle needs to cover the initial distance of 52.0 meters and then match the speed of the car, which is 21.5 m/s.
Let t be the time the motorcycle takes to cover the distance and catch up with the car.
We can set up an equation: distance = speed * time
Plugging in the values:
52 + 21.5 * t = 126
Rearranging the equation:
21.5 * t = 126 - 52
21.5 * t = 74
t = 74 / 21.5
t ≈ 3.44 s
Step 3: Calculate t2 - t1.
t2 - t1 = 3.44 s - 4.00 s
t2 - t1 ≈ -0.56 s
Therefore, it takes approximately -0.56 seconds from the moment the motorcycle starts to accelerate until it catches up with the car.