Question

An object has no forces acting upon it other than the one you exert. You apply a force over a given distance and as a result, the object winds up with speed v. Suppose you had applied twice the force over the same distance.

What would be the object's speed under this condition?
1.20
3. Impossible to say from the information given.
4. The same, v
5. V2v
6. 4v

Answer 1

Applying twice the force over the same distance results in the object ending up with twice the original speed, due to the direct relationship between the force and the final speed from the work-energy principle.

Step-by-step explanation:

When you exert twice the force over the same distance on an object, the final speed of the object would be greater than the initial speed v. According to the work-energy theorem, the work done on the object is equal to the change in kinetic energy (Work = ∆KE).

Since work is the product of force and distance (Work = Force x Distance), doubling the force while keeping the distance constant doubles the work done on the object. The change in kinetic energy, which is ½ mass x speed squared (∆KE = ½ mv2), would then be four times greater because, with constant mass, if the work done is doubled then the square of the final speed must be four times larger to balance the equation.

Therefore, the object's final speed when twice the force is applied over the same distance would be 2v, twice the original speed.