Answer :
Final answer:
The work required to increase the speed of a 1500 kg car from 30 km/h to 60 km/h is calculated by finding the change in kinetic energy, which is approximately 156250J. So the correct answer is option b. 156250J.
Explanation:
The amount of work done to change the velocity of a car can be calculated using the work-energy principle which states that work done is equal to the change in kinetic energy. The kinetic energy (KE) of an object is given by the equation: KE = (1/2)mv², where m is the mass of the object and v is its velocity. To find the work done to increase the velocity of a 1500 kg car from 30 km/h to 60 km/h, we first convert the speeds to meters per second (m/s) and then calculate the difference in kinetic energy.
To convert from km/h to m/s, multiply by (1000 m / 1 km) and divide by (3600 s / 1 h): 30 km/h = (30 * 1000) / 3600 ≈ 8.33 m/s , 60 km/h = (60 * 1000) / 3600 ≈ 16.67 m/s
Now, calculate the initial kinetic energy at 30 km/h and the final kinetic energy at 60 km/h: KE_initial = (1/2) * 1500 kg * (8.33 m/s)² ≈ 52083.125 J, KE_final = (1/2) * 1500 kg * (16.67 m/s)² ≈ 208332.5 J
The work done (W) is the change in kinetic energy:
W = KE_final - KE_initial ≈ 208332.5 J - 52083.125 J ≈ 156249.375 J
Therefore, the correct option is 156250J, which is closest to the calculated value and fits the options provided.
