A truck driver slams on the brakes and the momentum of the truck changes from ‹ 53000, 0, 0 › kg · m/s to ‹ 27000, 0, 0 › kg · m/s in 3.3 seconds due to a constant force of the road on the wheels of car. As a vector, write the net force exerted on the truck by the surroundings.

To find the net force exerted on the truck by the surroundings, we can use the principle of Newton's second law of motion, which states that the net force acting on an object is equal to the rate of change of its momentum.

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v):

p = m * v

Given the initial and final momenta:

Initial momentum (p₁) = ‹ 53000, 0, 0 › kg·m/s
Final momentum (p₂) = ‹ 27000, 0, 0 › kg·m/s

The change in momentum (Δp) can be calculated as:

Δp = p₂ - p₁

Let's calculate the change in momentum:

Δp = ‹ 27000, 0, 0 › - ‹ 53000, 0, 0 ›
= ‹ -26000, 0, 0 › kg·m/s

Now, we can use Newton's second law to find the net force exerted on the truck. Dividing the change in momentum by the time taken (t) will give us the net force (F):

F = Δp / t

Given the time taken (t) is 3.3 seconds, let's calculate the net force:

F = ‹ -26000, 0, 0 › kg·m/s / 3.3 s
= ‹ -7878.8, 0, 0 › N (Newton)

Therefore, as a vector, the net force exerted on the truck by the surroundings is ‹ -7878.8, 0, 0 › N (Newton).

To find the net force exerted on the truck by the surroundings, we can use the principle of impulse and momentum. The change in momentum (∆p) is equal to the net force (F) multiplied by the time interval (∆t).

∆p = F * ∆t

Given:
Initial momentum (p₁) = ‹ 53000, 0, 0 › kg · m/s
Final momentum (p₂) = ‹ 27000, 0, 0 › kg · m/s
Time interval (∆t) = 3.3 seconds

First, calculate the change in momentum:

∆p = p₂ - p₁
∆p = ‹27000, 0, 0› - ‹53000, 0, 0›
∆p = ‹-26000, 0, 0› kg · m/s

Next, divide the change in momentum (∆p) by the time interval (∆t) to find the net force:

F = ∆p / ∆t
F = ‹-26000, 0, 0› kg · m/s / 3.3 s
F = ‹-7878.79, 0, 0› N

Therefore, as a vector, the net force exerted on the truck by the surroundings is ‹-7878.79, 0, 0› N.