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

Guest Feb 6, 2015

#1**+5 **

**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{

$W=350\ J$

}}$$

heureka
Feb 6, 2015

#1**+5 **

Best Answer

**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{

$W=350\ J$

}}$$

heureka
Feb 6, 2015