Answer:
Step-by-step explanation:
To analyze the motion of the car, we can break down the given information into different phases: acceleration, coasting, and deceleration.
1. Acceleration phase:
The car accelerates at a rate of 2.0 m/s^2 for a duration of 6.7 seconds. This means that every second, the car's velocity increases by 2.0 m/s. To find the final velocity at the end of this phase, we can use the equation:
final velocity = initial velocity + (acceleration * time)
Since the car starts from rest (initial velocity = 0), the final velocity after 6.7 seconds of acceleration would be:
final velocity = 0 + (2.0 * 6.7) = 13.4 m/s.
2. Coasting phase:
After the acceleration phase, the car coasts for 2.1 seconds. During this phase, the car maintains a constant velocity. Therefore, the velocity remains at 13.4 m/s throughout the coasting phase.
3. Deceleration phase:
The car then slows down at a rate of 1.5 m/s^2. To find the time it takes for the car to come to a stop, we can use the equation:
final velocity = initial velocity + (acceleration * time)
Since the final velocity at the end of this phase is 0, and the initial velocity is 13.4 m/s, we can solve for the time it takes to decelerate to a stop:
0 = 13.4 + (-1.5 * time)
-13.4 = -1.5 * time
time = 8.93 seconds.
Therefore, the car takes a total of 6.7 seconds for acceleration, 2.1 seconds for coasting, and 8.93 seconds for deceleration to come to a stop at the next stop sign.