physics

A bicyclist was moving at a rate of 3 m/s, and then sped up to 4 m/s.

If the cyclist has a mass of 100 kg, how much work was needed to increase his velocity ?

$$\small{\text{
$
v_1 = 3\frac{m}{s} \qquad v_2 = 4\frac{m}{s} \qquad m = 100\ kg
$
}}$$

$$\\ \small{\text{
$
\boxed{ W=\Delta E_k=\frac12mv_2^2-\frac12mv_1^2=\frac12m (v_2^2-v_1^2)} , \qquad$
$E_k = $kinetic energy
}}\\
\small{\text{
where $v_1$ and $v_2$ are the speeds of the particle before and after the work is done and m is its mass.
}}\\\\
\small{\text{
$ \boxed { W=\frac12m (v_2^2-v_1^2)} $
}}\\\\
\small{\text{
$W=\frac12 *100*(4^2-3^2)\ \frac{kg*m^2}{s^2}$
}}\\
\small{\text{
$W=50*(16-9)\ \frac{kg*m^2}{s^2}$
}}\\
\small{\text{
$W=50*7\ \frac{kg*m^2}{s^2}$
}}\\
\small{\text{
$W=350\ \frac{kg*m^2}{s^2}$
}}\\
\small{\text{
$W=350\ J$
}}$$