Final answer:
The truck is in motion for a total of 35 seconds. The average speed of the truck is 14.29 m/s.
Step-by-step explanation:
The truck is in motion for the duration of the acceleration phase, the constant speed phase, and the braking phase. Let's calculate the time for each phase:
- Acceleration Phase: To find the time taken during the acceleration phase, we can use the equation v = u + at, where v is the final velocity (20 m/s), u is the initial velocity (0 m/s), a is the acceleration (2 m/s²), and t is the time taken. Rearranging the equation, we have t = (v - u) / a. Substituting the values, we get t = (20 - 0) / 2 = 10 seconds.
- Constant Speed Phase: The truck travels for 20 seconds at a constant speed, so the time taken for this phase is 20 seconds.
- Braking Phase: The truck stops in an additional 5 seconds.
To calculate the average speed, we need to find the total distance traveled by the truck. During the acceleration phase, the distance traveled can be found using the equation
s = ut + (1/2)at²,
where s is the distance traveled, u is the initial velocity, t is the time taken, and a is the acceleration.
Substituting the values, we get
s = 0 + (1/2)(2)(10)² = 100 meters.
During the constant speed phase, the distance traveled is speed multiplied by time, which is 20 m/s × 20 s = 400 meters.
During the braking phase, the truck comes to a stop, so the distance traveled is 0 meters. Therefore, the total distance traveled is 100 + 400 + 0 = 500 meters.
The average speed is given by total distance divided by total time.
The total time is the sum of the times taken during each phase, which is 10 s + 20 s + 5 s = 35 seconds.
Therefore, the average speed is 500 m / 35 s = 14.29 m/s.