Final answer:
The total time taken by the car from the first stop sign to the second stop sign is approximately 13.9 seconds.
Step-by-step explanation:
The total time taken by the car from the first stop sign to the second stop sign can be calculated by adding the times for acceleration, coasting, and deceleration.
For acceleration, we use the formula v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time. Rearranging the formula, we get t = (v - u) / a. Plugging in the values, t = (21.0 m/s - 0) / 3.7 m/s² = 5.68 s.
For coasting, the car travels at a constant speed, so the time is simply 2.2 s.
For deceleration, we use the same formula as acceleration, but with the final velocity as 0. Plugging in the values, t = (0 - 21.0 m/s) / (-3.5 m/s²) = 6.0 s.
Adding up the times for acceleration, coasting, and deceleration, we get 5.68 s + 2.2 s + 6.0 s = 13.88 s. Rounding to one decimal place, the total time taken by the car is approximately 13.9 seconds, which is closest to option 3) 13.4 s.