Read each statement below. For each situation, calculate vi, vf, pi, pf, the impulse vector F􏰁t, and the amount of force needed for the change to occur. All situations refer to a truck with a mass of 2840 kg

3.) The truck is at rest. In 5.00s, the truck backs up to a speed of 1.38m/s.

To solve this problem, we can use the basic principles of Newton's second law and the definition of impulse.

First, let's identify the given values:
- Mass of the truck (m): 2840 kg
- Initial velocity (vi) of the truck: 0 m/s (since it is at rest initially)
- Final velocity (vf) of the truck: 1.38 m/s
- Time (t): 5.00 s

Next, let's calculate the initial momentum (pi) of the truck. The formula for momentum (p) is given by:
p = m * v
where m is the mass and v is the velocity.

pi = m * vi
= 2840 kg * 0 m/s
= 0 kg·m/s

Since the truck is initially at rest, its initial momentum is 0 kg·m/s.

Now, let's calculate the final momentum (pf) of the truck. The formula for momentum is the same as above:

pf = m * vf
= 2840 kg * 1.38 m/s
= 3919.2 kg·m/s

The change in momentum (Δp) is given by:
Δp = pf - pi

Δp = 3919.2 kg·m/s - 0 kg·m/s
= 3919.2 kg·m/s

The impulse (Ft) experienced by the truck is equal to the change in momentum. The impulse can also be calculated using the formula:
Ft = Δp
= m * (vf - vi)

Ft = 2840 kg * (1.38 m/s - 0 m/s)
= 3919.2 kg·m/s

Finally, we can calculate the average force (F) exerted on the truck to produce this change in momentum. The formula for average force is:
F = Ft / t

F = 3919.2 kg·m/s / 5.00 s
= 783.84 N

Therefore, in order for the truck to back up to a speed of 1.38 m/s in 5.00 s, an average force of 783.84 N is required.