Question

the average power of an engine which accelerates a car of mass 1000 kg to a speed of 36 km/ hour from rest in 5 sec is​

Answer 1

Given:

• Mass = 1000 kg
• Velocity attained = 36 km/hr
• Initial velocity = 0 m/s
• Time taken = 5 sec

Calculation:

First of all, convert velocity value from km/hr to m/s:

• 1 km/hr = 5/18 m/s

• So, 36 km/hr = 36 × 5/18 = 10 m/s.

Now, power is rate of doing work. And work can be calculated from WORK-ENERGY THEOREM.

• The theorem states that work done by a force is equal to the change in kinetic energy of the object.

$\therefore \: P = \dfrac{W}{t}$

$\implies \: P = \dfrac{\Delta KE}{t}$

$\implies \: P = \dfrac{ \dfrac{1}{2}m {v}^{2} - \dfrac{1}{2} m {u}^{2} }{t}$

$\implies \: P = \dfrac{ \dfrac{1}{2}(1000) {(10)}^{2} - \dfrac{1}{2} m {(0)}^{2} }{5}$

$\implies \: P = \dfrac{(1000) {(10)}^{2} }{10}$

$\implies \: P = 10000 \: watt$

$\implies \: P = 10 \: kilowatt$

So, power delivered by object is 10 kW.