How does work relate to speed?

1 Answer
Oct 25, 2015

Answer:

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!