Final answer:
The braking force exerted by the truck is found by using the impulse-momentum theorem and calculating the change in momentum, which is then divided by the time over which the force is applied. The calculated force is -17596.3 N, indicating it acts opposite to the direction of the truck's motion.
Step-by-step explanation:
To determine the braking force exerted by the truck, we need to use the impulse-momentum theorem, which states that the change in momentum (Δp) of an object is equal to the impulse (J) applied to it. The formula for impulse is J = FΔt, where F is the force applied and Δt is the time over which the force is applied. We also know that Δp = mvf - mvi, where m is the mass of the truck, vf is the final velocity, and vi is the initial velocity.
First, we convert the weight of the truck from pounds to kilograms, knowing that 1 lb = 0.453592 kg.
m = 17926 lb * 0.453592 kg/lb = 8127.81 kg
Then, we calculate the change in velocity:
Δv = vf - vi = 30.3 ft/s - 75.6 ft/s = -45.3 ft/s
Note that we take the initial velocity vi to be positive and the final velocity vf to be smaller, which indicates a decrease in speed due to braking, hence the negative sign in the change of velocity.
Next, we calculate the change in momentum (Δp):
Δp = m(vf - vi) = 8127.81 kg * (-45.3 ft/s * 0.3048 m/ft)
Δp = -112614.3 kg*m/s (after converting feet to meters)
Finally, we find the impulse (J):
J = Δp = FΔt
So, the force (F) can be found by rearranging the formula:
F = J/Δt = -112614.3 kg*m/s / 6.4 s
F = -17596.3 N (Note that the force is negative because it is in the direction opposite to the truck's initial motion.)
This is the braking force applied by the truck to reduce its speed.