A car starts from rest, accelerating at 6.0 m/s for 5s. It continues at this speed for 25s, and then comes to a stop in 4s. Calculate (a) total distance covered, and (b) the average velocity for the whole displacement.
To solve this problem, we can break it down into three parts: the initial acceleration, the constant velocity, and the deceleration.
(a) Total distance covered:
For the initial acceleration, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car starts from rest, the initial velocity is 0 m/s. Therefore, the distance covered during the initial acceleration is:
distance = (0 * 5) + (0.5 * 6.0 * 5^2)
distance = 0 + (0.5 * 6.0 * 25)
distance = 0 + 75
distance = 75 meters
During the constant velocity phase, the car is traveling at 6.0 m/s for 25 seconds, so the distance covered is:
distance = velocity * time
distance = 6.0 * 25
distance = 150 meters
Finally, during the deceleration phase, the car comes to a stop in 4 seconds. We can use the same formula as before, but with a negative acceleration value since the car is decelerating:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
distance = (6.0 * 4) + (0.5 * -6.0 * 4^2)
distance = 24 + (-24)
distance = 0 meters
The total distance covered is the sum of the distances covered during each phase:
Total distance = 75 + 150 + 0
Total distance = 225 meters
(b) Average velocity for the whole displacement:
The average velocity is given by the formula:
average velocity = total displacement / total time
The total displacement is the change in position from the initial point to the final point, which is 0 meters since the car starts and ends at the same position.
The total time is the sum of the times for each phase:
Total time = initial acceleration time + constant velocity time + deceleration time
Total time = 5 + 25 + 4
Total time = 34 seconds
Therefore, the average velocity for the whole displacement is:
average velocity = total displacement / total time
average velocity = 0 / 34
average velocity = 0 m/s