Question

A car of mass 1000 kg accelerates from rest to $100km{h}^{-1}$ in 5 seconds. What is the average power of the car ?

• A. $7.71\times {10}^{5}W$
• B. $7.71\times {10}^{4}W$
• C. $15.42\times {10}^{4}W$
• D. $15.42\times {10}^{5}W$

Answer 1

Answer: (B)

$7.71\times {10}^{4}W$

Mass of the car m$=1000kg$

Initial velocity of car $v_1=0$

Final velocity of car $v_2$$=100km/h=100\times \frac{5}{18}m/s=27.78m/s$

Average power of car$=$change in kinetic energy per unit time$=\frac{\frac{1}{2}m{v_2}^2-\frac{1}{2}m{v_1}^2}{t}$,since $v_1=0$

So,average power of car$=\frac{\frac{1}{2}m{v_2}^2}{t}$

$=\frac{\frac{1}{2}\times 1000\times {27.78}^2}{5}$

$=7.71\times {10}^{4}W$