Solve it kindly?

Question

Solve it kindly?

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

1 Answer

Impact of this question

2083 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-13T03:44:53

$W = \frac{8}{3}$ $W = 8/3$ $J$ $"J"$

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 $W$ $W$ done in a particle is the dot product of the force and displacement vectors:

$W = \to F ∙ \to s$ $W = vecF • vecs$

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

$W = F s$ $W = Fs$

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

$s = \frac{{(2)}^{2}}{3} = \frac{4}{3}$ $s = ((2)^2)/3 = 4/3$ $m$ $"m"$

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:

$\frac{d^{2}}{{d t}^{2}} [\frac{t^{2}}{3}] = \frac{2}{3}$ $(d^2)/(dt^2) [(t^2)/3] = 2/3$

So the acceleration $a$ $a$ is constant at $\frac{2}{3}$ $2/3$ ${m/s}^{2}$ $"m/s"^2$ .

The force $F$ $F$ that acts is

$F = m a = (3 l kg) (\frac{2}{3} l {m/s}^{2}) = 2$ $F = ma = (3color(white)(l)"kg")(2/3color(white)(l)"m/s"^2) = color(red)(2$ $N$ $color(red)("N"$

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

$W = (2 l N) (\frac{4}{3} l m) = \frac{8}{3}$ $W = (color(red)(2)color(white)(l)color(red)("N"))(4/3color(white)(l)"m") = color(blue)(8/3$ $J$ $color(blue)("J"$

Science

Math

Humanities

... and beyond

Solve it kindly?

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Solve it kindly?

A body of mass 3kg is under a force causes a displacement in it ,given by S=t^2/3S=t23S=t^2/3(in meters). The work done by the force in 2s is what?

1 Answer

Explanation:

Related questions

Impact of this question

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