Final answer:
The truck accelerates for 10.0 seconds until it reaches a speed of 20.0 m/s, and then it travels at a constant speed for an additional 5.00 seconds until it stops. Therefore, the truck is in motion for a total of 15.0 seconds.
Step-by-step explanation:
The truck is initially accelerating at a rate of 2.00 m/s² until it reaches a speed of 20.0 m/s. This acceleration lasts for a certain amount of time, which we can determine using the equation:
vf = vi + at
Where:
- vf is the final velocity (20.0 m/s)
- vi is the initial velocity (0 m/s)
- a is the acceleration (2.00 m/s²)
- t is the time
Substituting the known values into the equation, we can solve for t:
20.0 m/s = 0 m/s + 2.00 m/s² * t
Simplifying the equation, we get:
t = 20.0 m/s / 2.00 m/s²
t = 10.0 s
So, the truck accelerates for 10.0 seconds until it reaches a speed of 20.0 m/s.
After reaching this speed, the truck travels at a constant speed for a certain amount of time until the brakes are applied. We know that the truck stops in an additional 5.00 seconds, so the total time the truck is in motion can be calculated by summing the time it took to accelerate and the additional time to stop:
Total time in motion = Acceleration time + Stopping time
Total time in motion = 10.0 s + 5.00 s
Total time in motion = 15.0 s
Therefore, the truck is in motion for a total of 15.0 seconds.