A truck of mass 8,000 kg is traveling along a level road at an initial speed of 25 m/s. The driver then shifts into neutral so that the truck is coasting, and the truck gradually slows to a final speed of 13 m/s.

(a) Find the total work done on the truck.

the work is equal to the change in the (kinetic) energy of the truck

w = (1/2 m 25^2) - (1/2 m 13^2)

w = 1/2 * 8000 * (25^2 - 13^2)

To find the total work done on the truck, we need to use the work-energy principle. The work-energy principle states that the net work done on an object is equal to its change in kinetic energy.

The formula for work is given by:
Work = Force x Distance x cos(θ)

Since the truck is coasting on a level road, there is no change in height, so the work done against gravity is zero. Additionally, since the truck is in neutral, there is no engine force or applied force.

Therefore, the only force acting on the truck is the force of friction. We can calculate the work done by friction by using the formula for work mentioned above.

The net force acting on the truck is given by:
Net Force = Mass x Acceleration

We can calculate the acceleration of the truck using the kinematic equation:
(v² - u²) = 2as

Where:
v = final velocity = 13 m/s
u = initial velocity = 25 m/s
a = acceleration
s = distance

Rearranging the equation to solve for acceleration (a), we have:
a = (v² - u²) / (2s)

Now, let's calculate the acceleration of the truck.

a = (13² - 25²) / (2s)

To determine the distance traveled as the truck slows down from the initial speed to the final speed, we need to calculate the average speed and time taken during that interval.

Average speed = (initial speed + final speed) / 2
Average speed = (25 + 13) / 2 = 19 m/s

To calculate the time taken, we can use the formula:
Time = Distance / Average speed

Assuming the time taken is 5 seconds, we can calculate the distance traveled by the truck as follows:

Distance = Average speed x Time
Distance = 19 m/s x 5 s = 95 meters

Now that we have the acceleration (a) and the distance (s), we can find the net force acting on the truck:

Net Force = Mass x Acceleration
Net Force = 8000 kg x a

Finally, we can calculate the work done by friction:

Work = Force x Distance x cos(θ)
Work = Net Force x Distance x cos(θ)
Work = 8000 kg x a x 95 m x cos(180)

Since the truck is coasting in neutral, the angle (θ) between the force of friction and the displacement is 180 degrees, so the cos(θ) term becomes -1.

Work = 8000 kg x a x 95 m x (-1)

Now, you can substitute the calculated values of acceleration (a) and solve for the net work done on the truck.