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?

1 Answer
Jul 13, 2017

Answer:

#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"#