Did you know?
Did you know that in a scenario where a car starts from rest and accelerates uniformly until it reaches a velocity of 30m/s after 5 seconds, it then travels with a constant velocity for 15 seconds, and finally comes to a stop in 10 seconds with a uniform deceleration, we can determine various aspects of the car's motion?
To find the acceleration of the car, we need to calculate the change in velocity divided by the change in time. In this case, the change in velocity is 30m/s (from rest to 30m/s) and the change in time is 5 seconds. Therefore, the acceleration of the car is 6m/s^2.
Similarly, to determine the retardation (or deceleration), we can calculate the change in velocity divided by the change in time. The change in velocity is 30m/s (from the constant velocity to rest) and the change in time is 10 seconds. Hence, the retardation is -3m/s^2 (negative due to deceleration).
The distance covered after 5 seconds can be found using the equation of motion: distance = initial velocity * time + 0.5 * acceleration * time^2. Since the car starts from rest, the initial velocity is 0m/s. Plugging in the values, we get distance = 0 + 0.5 * 6m/s^2 * (5s)^2, which simplifies to 75 meters.
To calculate the total distance covered, we need to consider the different stages of motion. For the initial acceleration, we can use the equation of motion: distance = initial velocity * time + 0.5 * acceleration * time^2. In this case, the initial velocity is 0m/s, the acceleration is 6m/s^2, and the time is 5 seconds. Hence, distance = 0 + 0.5 * 6m/s^2 * (5s)^2, which equals 75 meters.
For the constant velocity stage, we multiply the velocity (30m/s) by the time (15 seconds) to get a distance of 450 meters.
Finally, for the deceleration, we can again use the equation of motion: distance = initial velocity * time + 0.5 * acceleration * time^2. Now, the initial velocity is 30m/s, the acceleration is -3m/s^2 (deceleration is negative), and the time is 10 seconds. Plugging in the values, we get distance = 30m/s * 10s + 0.5 * -3m/s^2 * (10s)^2, which simplifies to 150 - 150 meters, resulting in 0 meters (since the car comes to rest).
Therefore, the total distance covered by the car in this scenario is 75 meters + 450 meters + 0 meters, which equals 525 meters.
