The problem requires calculating the work done to increase the speed of a car, which can be found using the work-energy theorem. The work done is equal to the change in kinetic energy.

Work-Energy Theorem Application

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy: \(W = \Delta KE = KE_f - KE_i\).

Given Data

• Mass of the car (\(m\)): 800 Kg
• Initial speed (\(v_i\)): 54 km/hr
• Final speed (\(v_f\)): 90 km/hr

Speed Conversion

First, convert the speeds from km/hr to m/s:

• \(v_i = 54 \text{ km/hr} = 54 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 15\) m/s
• \(v_f = 90 \text{ km/hr} = 90 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 25\) m/s

Kinetic Energy Calculation

Calculate the initial and final kinetic energies using the formula \(KE = \frac{1}{2} m v^2\).

• Initial Kinetic Energy (\(KE_i\)): \(KE_i = \frac{1}{2} \times 800 \text{ Kg} \times (15 \text{ m/s})^2 = 400 \times 225 = 90000\) J
• Final Kinetic Energy (\(KE_f\)): \(KE_f = \frac{1}{2} \times 800 \text{ Kg} \times (25 \text{ m/s})^2 = 400 \times 625 = 250000\) J

Work Done Calculation

Now, calculate the work done by finding the difference between the final and initial kinetic energies:

• Work Done (\(W\)): \(W = KE_f - KE_i = 250000 \text{ J} - 90000 \text{ J} = 160000\) J

Convert the work done to kilojoules (KJ):

• \(W = 160000 \text{ J} = 160\) KJ

Conclusion

The work required to be done to increase the speed of the car is 160 KJ.