Question

Solve it kindly?

A body of mass 3kg is under a force causes a displacement in it ,given by `S=t^2/3`(in meters). The work done by the force in 2s is what?

Answer 1

`W = 8/3` `"J"`

Explanation:

We're asked to find the work done on a particle given its mass and position equation with time.

I'll solve it without using kinetic energy formulas, but via force and displacement. Take a look at The Useful G.'s response for a different approach.

The equation for the work `W` done in a particle is the dot product of the force and displacement vectors:

`W = vecF • vecs`

Since his motion is one-dimensional, we can also write this as

`W = Fs`

We can find the object's displacement at time `t = 2` `"s"` by plugging #`in for`t# in the equation:

`s = ((2)^2)/3 = 4/3` `"m"`

To find the constant force that acts on the object, we can first find the acceleration as a function of time, by differentiating the position equation twice:

`(d^2)/(dt^2) [(t^2)/3] = 2/3`

So the acceleration `a` is constant at `2/3` `"m/s"^2`.

The force `F` that acts is

`F = ma = (3color(white)(l)"kg")(2/3color(white)(l)"m/s"^2) = color(red)(2` `color(red)("N"`

Now that we know the force `F` and displacement `s`, the work done by the force during this time is

`W = (color(red)(2)color(white)(l)color(red)("N"))(4/3color(white)(l)"m") = color(blue)(8/3` `color(blue)("J"`