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TheronSimon · Dec 11, 2011, 10:00 AM

I don't understand how to calculate this question, it would be great if anyone could help

Aurora2000 · Dec 12, 2011, 09:20 AM

The work done is not dependent on time. You can determine it by using the difference
of kinetic energy, thus

$Work= \frac{1}{2}mv^2-\frac{1}{2}mv_0^2$

where m is the mass (in your case m=2.0 kg), $v$ the final speed (here 3.0 m/s)
and $v_0$ the initial speed (here 2.0 m/s)

TheronSimon · Dec 12, 2011, 06:39 PM

Its acceleration not velocity, but thanks I already figured it out

ebaines · Dec 13, 2011, 07:59 AM

Aurora's approach is correct and the most direct way to find the work done. An alternative, more complicated approach is to determine the acceleration, from that the force applied, and multiply that by the distance traveled during application of that force. You will find that the acceleration component cancels out (hence no need for time), as Aurora suggests - all that matters is the mass and its change in velocity. Here's the math:

$<br /> F = ma\\<br /> d = \frac {v^2 - v_0^2} {2a} \\<br /> W = Fd = m a \frac {(v^2 - v_0^2)} {2 a} = \frac 1 2 m (v^2 - v_0^2)<br />$