If the work required to speed up a car from 13 km/h to 20 km/h is 6.5×103 J, what would be the work required to increase the car’s speed from 20 km/h to 35 km/h?
Multiply 6.5*10^3 J by the ratio
[35^2 - 20^2]/[20^2 - 13^2]
That is the ratio of the kinetic energy increases in the two cases.
To determine the work required to increase the car's speed from 20 km/h to 35 km/h, we need to use the concept of kinetic energy. The work done on an object is equal to the change in kinetic energy.
The formula for kinetic energy is:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Since we're dealing with a car, we can assume the mass remains constant. So, we can disregard the mass and focus solely on the change in velocity.
To calculate the work required to increase the car's speed from 20 km/h to 35 km/h, we first need to find the change in kinetic energy.
Step 1: Convert the velocities from km/h to m/s.
- 20 km/h = (20 * 1000 m) / (60 * 60 s) = 5.56 m/s
- 35 km/h = (35 * 1000 m) / (60 * 60 s) = 9.72 m/s
Step 2: Calculate the change in kinetic energy.
- ΔKE = 0.5 * m * (vf^2 - vi^2)
- ΔKE = 0.5 * (9.72^2 - 5.56^2)
- ΔKE = 0.5 * (94.46 - 30.94)
- ΔKE = 0.5 * 63.52
- ΔKE = 31.76 Joules
Therefore, the work required to increase the car's speed from 20 km/h to 35 km/h is approximately 31.76 J.