+0  
 
0
336
1
avatar

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

Best Answer 

 #1
avatar+19207 
+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
Sort: 

1+0 Answers

 #1
avatar+19207 
+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

31 Online Users

avatar
avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details