Question

How does work relate to speed?

Answer 1

It could be through the Work and Kinetic Energy theorem:

Explanation:

Consider a constant force `vecF` acting on an object of mass `m` for a distance `d` along the `x` axis only and producing an acceleration `a`;
work will be:

`W=F*d==ma*d` (from Newton's Law);

We can use cinematics to relate final and initial velocity to distance and accekeration as:

`v_f^2=v_i^2+2ad`
And
`ad=(v_f^2-v_i^2)/2`
Substituting into the expression for work:
`W= m(v_f^2-v_i^2)/2=1/2m v_f^2-1/2mv_i^2=DeltaK`
Where `K` is Kinetic Energy!