Question

A 400 kg car from rest attains a speed of 50 m/s in 20 s. Find the power developed in the engine​

Answer 1

Answer:

power = work/time use this formula u get ans

Answer 2

Given:-

• Mass of car ( m ) = 400 kg

• Initial velocity of car ( u ) = 0 m/s

• Final velocity of car ( v ) = 50 m/s

• Time elapsed ( t ) = 20 sec

To Find:-

• Power developed in the engine.

Solution:-

Here, Power = $\dfrac{W}{t}$                  Where, W = work-done,

                                                            t = time elapsed

Now, Work-Done = F × S                       Where,  F = Force

                                                                              S = Displacement

So, Force applied by engine ⇒ m × a

                                                ⇒ 400 × $\bigg(\dfrac{50 - 0}{20}\bigg)$

                                                ⇒ 1000 N

∵ Acceleration of car ( a ) ⇒ $\bigg (\dfrac{v - u}{t}\bigg)$

                                          ⇒ $\bigg (\dfrac{50 - 0}{20}\bigg)$

                                          ⇒ $\dfrac{5}{2}$ m/s²

Now, By second equation of motion

⇒ $S = ut + \dfrac{1}{2}at^{2}$

⇒ $S = 0 \times 20 + \dfrac{1}{2} \times \dfrac{5}{2} \times 20 \times 20$

⇒ $S = \dfrac{1}{2} \times \dfrac{5}{2} \times 20 \times 20$                             [ If any number is multiplied with 0 it product will be 0]

⇒ $S = 500 \ m$

So, Work-Done ⇒ F × S

                          ⇒ 1000 N × 500 m

                          ⇒ 5,00,000 joule

∴ Power of the Engine ⇒ $\dfrac{W}{t}$

                                      ⇒ $\dfrac{5,00,000}{20}$

                                      ⇒ 25,000 watt

We know that 1kW = 1000 watt

         25,000 watt = $\dfrac{25,000}{1000}$ = 25 kW

                         

Hence, Power developed in the Engine is 25,000 watt or 25kilowatt.

Some Important terms:-

• Power = $\dfrac{W}{t}$

• Work-Done = F × S

• Kinetic Energy = $\dfrac{1}{2}mv^{2}$

• Potential Energy = $mgh$                       Where, m = mass of the body

                                                                           g = acceleration due to gravity

                                                                             h = height from the ground