Question

The velocity of an object with mass = 2kg is given as a function of time:

V = 2ti + 4
`t^(2)`j

Find the force acting on the object at t = 2 seconds.

Answer 1

The force acting on the object at
`t = 2\,s` is
`\vec F = (4, 32)\,[N]`.

Step-by-step explanation:

Given that object has a constant mass in time, the force acting on the object (
`\vec F`), in newtons, is defined by following expression:

`\vec F = m\cdot \vec a` (1)

Where:

`m` - Mass, in kilograms.

`\vec a` - Acceleration, in meters per square second.

By definition of acceleration, we know that:

`\vec a = (d)/(dt) \vec v` (2)

Let suppose that given vector velocity is expressed in meters per second. If we know that
`m = 2\,kg`,
`\vec v = (2\cdot t, 4\cdot t^(2))\,\left[(m)/(s) \right]` and
`t = 2\,s`, then the force acting on the object is:

`\vec a = (2, 8\cdot t)\,\left[(m)/(s^(2)) \right]`

`\vec F = (4, 16\cdot t)\,[N]`

`\vec F = (4, 32)\,[N]`

The force acting on the object at
`t = 2\,s` is
`\vec F = (4, 32)\,[N]`.