What is the work done by a car's braking system when it slows the 1500-kg car from an initial speed of 96 km/h down to 56 km/h in a distance of 55 m?

I have tried to work this one and can't seem to get the answer.

The work of the brakes will result in a change in kinetic energy:

W = ΔK
W = ½mv² - ½mv₀²
W = ½m(v² - v₀²)

First, convert units from km/h to m/s:
v₀ = 96km/h (1000m / 1km × 1h / 3600s) = 26.67 m/s
v = 56km/h (1000m / 1km × 1h / 3600s) = 15.56 m/s

Substitute in equation:
W = ½m(v² - v₀²)
W = ½1500kg [(15.56m/s)² - (26.67m/s)²].
W = -351881.475 J ≈ - 3.5 × 10⁵ J

Well, let's dive into the world of physics with a dash of humor! The work done by the car's braking system can be calculated using the work-energy principle, which states that the work done equals the change in kinetic energy.

To get started, we need to calculate the initial and final kinetic energies of the car. The initial kinetic energy can be found using the formula KE = 1/2 * m * v^2, where m is the mass of the car and v is the initial velocity. Plugging in the values, we have KE_initial = 1/2 * 1500 kg * (96 km/h)^2.

The final kinetic energy can be found using the same formula, but with the final velocity. So, KE_final = 1/2 * 1500 kg * (56 km/h)^2.

Now, let's calculate the work done. The work done is equal to the change in kinetic energy, so Work = KE_final - KE_initial. Plug in the values, and you've got the work done by the braking system!

But hey, even with all these calculations, I have to say that 1500 kg car going from 96 km/h to 56 km/h in just 55 meters must be in quite a hurry to stop! I hope it didn't have a date with a traffic ticket. Remember to drive safe, and let the braking system do the work!

To find the work done by a car's braking system, you need to calculate the change in kinetic energy of the car.

The formula for kinetic energy is:

KE = 1/2 * m * v^2

Where KE is the kinetic energy, m is the mass of the car, and v is the velocity of the car.

First, we need to convert the speeds from km/h to m/s:

Initial speed = 96 km/h = (96 * 1000) / (60 * 60) = 26.67 m/s
Final speed = 56 km/h = (56 * 1000) / (60 * 60) = 15.56 m/s

Next, we calculate the initial kinetic energy:

KE_initial = 1/2 * m * v_initial^2
KE_initial = 1/2 * 1500 kg * (26.67 m/s)^2
KE_initial = 559,894.45 J

Then, we calculate the final kinetic energy:

KE_final = 1/2 * m * v_final^2
KE_final = 1/2 * 1500 kg * (15.56 m/s)^2
KE_final = 181,670.56 J

Finally, we calculate the work done by subtracting the final kinetic energy from the initial kinetic energy:

Work done = KE_final - KE_initial
Work done = 181,670.56 J - 559,894.45 J
Work done = -378,223.89 J

The negative sign indicates that the work done by the braking system is negative, meaning the braking system is doing work on the car to slow it down.

Therefore, the work done by the car's braking system is approximately -378,223.89 J.

20kj