A car is moving with velocity 25km/hr. After 10 minutes its velovity changes to 100km/hr. How much kinetic energy changed? If mass of the car is 2000 kg, what will be the work done to change its velocity?
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A car is moving with velocity 25km/hr. After 10 minutes its velovity changes to 100km/hr. How much kinetic energy changed? If mass of the car is 2000 kg, what will be the work done to change its velocity?
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Answer:
To find the change in kinetic energy and the work done to change the car's velocity, you can use the following formulas:
1. Change in Kinetic Energy (ΔKE):
ΔKE = 0.5 * m * (vf^2 - vi^2)
Where:
- ΔKE is the change in kinetic energy.
- m is the mass of the car (2000 kg).
- vf is the final velocity (100 km/hr converted to m/s).
- vi is the initial velocity (25 km/hr converted to m/s).
2. Work Done (W):
W = ΔKE
Let's calculate it step by step:
First, convert the velocities from km/hr to m/s:
- Initial velocity (vi) = 25 km/hr = (25 * 1000 m) / (3600 s) = 6.94 m/s (rounded to two decimal places).
- Final velocity (vf) = 100 km/hr = (100 * 1000 m) / (3600 s) = 27.78 m/s (rounded to two decimal places).
Now, plug these values into the formulas:
1. ΔKE = 0.5 * 2000 kg * (27.78 m/s)^2 - (6.94 m/s)^2)
2. ΔKE = 0.5 * 2000 kg * (771.88 m^2/s^2 - 48.13 m^2/s^2)
3. ΔKE = 0.5 * 2000 kg * 723.75 m^2/s^2
4. ΔKE = 723750 J (joules)
So, the change in kinetic energy is 723750 joules, and this is also the work done to change the car's velocity.