Here's how to rearrange the formula and solve for distance:
1. Work-Energy Theorem:
* Work (W) = Change in Kinetic Energy (ΔKE)
2. Work and Force Relationship:
* Work (W) = Force (F) x Distance (d)
3. Combining the Equations:
* F x d = ΔKE
4. Solving for Distance:
* d = ΔKE / F
Therefore, to find the distance, you need to know the change in kinetic energy and the force applied.
Here's a breakdown of the variables:
* Work (W): The amount of energy transferred to or from an object by a force. Measured in Joules (J).
* Force (F): A push or pull that can change an object's motion. Measured in Newtons (N).
* Distance (d): The length over which the force acts. Measured in meters (m).
* Change in Kinetic Energy (ΔKE): The difference between the object's final kinetic energy and its initial kinetic energy. Measured in Joules (J).
Example:
A 2000 kg car accelerates from rest to a speed of 10 m/s. What distance does the car travel during this acceleration if the engine exerts a force of 5000 N?
1. Calculate the change in kinetic energy:
* Initial KE = 0 (car is at rest)
* Final KE = (1/2) * 2000 kg * (10 m/s)² = 100,000 J
* ΔKE = 100,000 J - 0 J = 100,000 J
2. Calculate the distance:
* d = ΔKE / F = 100,000 J / 5000 N = 20 m
Therefore, the car travels 20 meters during the acceleration.
