Question

If a `2 kg` object is being constantly accelerated from `0m/s` to `15 m/s` over `6s`, how much power is being applied at `t= 3`?

Answer 1

P = 19 W

Explanation:

To solve this problem we will first find the value of acceleration involved, then use that to determine the resultant force required to produce that acceleration, then find the velocity at 3 s, and lastly calculate the power.

The object has a constant acceleration so the force is constant and the equations of uniform acceleration can be used.

1. Calculate the acceleration.
`s =?`
`u = 0`
`v = 15 m.s^(-1)`
`a =?`
`t = 6 s`
Use `v = u + at ⇒ a = (v-u)/t`
`⇒ a = (15-0)/6= 2.5 m.s^(-2)`

2. Resultant force.
`F=ma = 2× 2.5 = 5.0 N`

3. Velocity at 3 s.
We can use an equation of constant acceleration to determine the velocity of the object at 3 seconds.
`v= u + at = 0 + 2.5 × 3 = 7.5 m s^(-1)`

4. Power.
`P = Fv = 5.0 × 7.5 = 37.5 = 38 W` (2 sf)