The force applied to an object to accelerate it from 7m/s to 11m/s can be calculated using the work-energy principle where work equals the change in kinetic energy. The force is then found by dividing the work by the distance over which the force is applied.
To calculate the force applied to accelerate an object from an initial velocity to a final velocity over a given distance, you can use the work-energy principle. The work done on the object is equal to the change in kinetic energy. The initial kinetic energy (KEi) is ½ × mass × (initial velocity)2, and the final kinetic energy (KEf) is ½ × mass × (final velocity)2. Thus, the work done (W) is KEf - KEi. Since work is also equal to force times distance (W = F × distance), we can solve for force (F) by dividing the work by the distance over which the force is applied.
For an object of mass 5kg, with an initial speed of 7m/s and a final speed of 11m/s over a distance of 2m, the calculation would be:
- Calculate the initial and final kinetic energies: KEi = ½ × 5kg × (7m/s)2, KEf = ½ × 5kg × (11m/s)2
- Find the change in kinetic energy: ΔKE = KEf - KEi
- Calculate work done, W = ΔKE
- Calculate force: F = W / distance
The exact force can then be found and expressed in newtons (N).