Final answer:
The car took 7 seconds to accelerate to 21.0 m/s and 5.25 seconds to decelerate to a stop, resulting in a total travel time of 12.25 seconds between the stop signs.
Step-by-step explanation:
To calculate the total time it took for the car to travel, we need to find the time taken for acceleration and deceleration separately and then sum them up. For acceleration, we use the formula time = final velocity / acceleration. The car accelerates to 21.0 m/s at a rate of 3.0 m/s2, so the time taken to accelerate is 21.0 m/s ÷ 3.0 m/s2 = 7 seconds.
For deceleration, we again use the formula time = final velocity / deceleration. However, the car is slowing down, so the final velocity is zero, and the initial velocity is the same as the final velocity from the acceleration phase, which is 21.0 m/s. Thus, the time to decelerate is 21.0 m/s ÷ 4.0 m/s2 = 5.25 seconds.
The total time taken for the trip is the sum of the acceleration and deceleration times: 7 seconds + 5.25 seconds = 12.25 seconds. Therefore, it took the car 12.25 seconds to travel from one stop sign to the other.