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# physics

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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

Feb 6, 2015

#1
+22358
+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 ?

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

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

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Feb 6, 2015

#1
+22358
+5
$$\small{\text{  v_1 = 3\frac{m}{s} \qquad v_2 = 4\frac{m}{s} \qquad m = 100\ kg  }}$$
$$\\ \small{\text{  \boxed{ W=\Delta E_k=\frac12mv_2^2-\frac12mv_1^2=\frac12m (v_2^2-v_1^2)} , \qquad E_k = kinetic energy }}\\ \small{\text{ where v_1 and v_2 are the speeds of the particle before and after the work is done and m is its mass. }}\\\\ \small{\text{  \boxed { W=\frac12m (v_2^2-v_1^2)}  }}\\\\ \small{\text{ W=\frac12 *100*(4^2-3^2)\ \frac{kg*m^2}{s^2} }}\\ \small{\text{ W=50*(16-9)\ \frac{kg*m^2}{s^2} }}\\ \small{\text{ W=50*7\ \frac{kg*m^2}{s^2} }}\\ \small{\text{ W=350\ \frac{kg*m^2}{s^2} }}\\ \small{\text{ W=350\ J }}$$