A truck on a straight road starts from rest and accelerates at 3.0 m/s2 until it reaches a speed of 18.1 m/s. Then the truck travels for 24.5 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.7 s. (a) How long is the truck in motion?
V = Vo +a*t = 18.1 m/s.
0 + 3*t = 18.1
t1 = 6.03 s.
t2 = 24.5 s.
t3 = 5.7 s.
T = t1 + t2 + t3
T = 6.03 + 24.5 + 5.7 = 36.23 s.
To determine how long the truck is in motion, we need to calculate the time it takes for the truck to accelerate to its final speed, the time it travels at a constant speed, and the time it takes to stop.
1. Time to accelerate to final speed:
The initial velocity (u) of the truck is 0 m/s (as it starts from rest), the final velocity (v) is 18.1 m/s, and the acceleration (a) is 3.0 m/s². We can use the equation v = u + at to find the time it takes to accelerate to the final speed:
v = u + at
18.1 = 0 + 3.0t
3.0t = 18.1
t = 18.1 / 3.0
t ≈ 6.03 s
2. Time traveled at constant speed:
The truck travels at a constant speed for 24.5 seconds.
3. Time to stop:
The truck stops in 5.7 seconds.
To determine the total time the truck is in motion, we add the times from step 1, step 2, and step 3 together:
Total time = time to accelerate + time traveled at constant speed + time to stop
Total time = 6.03 s + 24.5 s + 5.7 s
Total time ≈ 36.23 seconds
Therefore, the truck is in motion for approximately 36.23 seconds.
To find out how long the truck is in motion, we need to calculate the total time it takes for the truck to accelerate to its final speed, travel at a constant speed, and then come to a stop.
First, let's find the time it takes for the truck to accelerate to its final speed of 18.1 m/s.
We can use the equation of motion:
v = u + at
Where:
v = final velocity (18.1 m/s)
u = initial velocity (0 m/s as the truck starts from rest)
a = acceleration (3.0 m/s²)
t = time
Rearranging the equation, we can solve for time:
t = (v - u) / a
t = (18.1 m/s - 0 m/s) / 3.0 m/s²
t = 18.1 s
So, it takes 18.1 seconds for the truck to accelerate to its final speed.
Next, let's calculate the time the truck travels at a constant speed of 18.1 m/s.
Given that the truck travels for 24.5 seconds at a constant speed, we already have this value.
Finally, we need to find the time it takes for the truck to come to a stop.
The braking time is given as 5.7 seconds.
Now, to find the total time the truck is in motion, we add these three times together:
Total time = Acceleration time + Constant speed time + Braking time
Total time = 18.1 s + 24.5 s + 5.7 s
Total time = 48.3 s
Therefore, the truck is in motion for 48.3 seconds.