Question

the power required by engine of car of mass 1000 kg to accelerate it from rest to a speed of 72km/h in 20s is
1)10 kW
2)1 kW
3)100 kW
4)1000 kW​

Answer 1

Given:-

→ Mass of the car = 1000kg

→ Initial velocity = 0

→ Final velocity = 72km/h = 20m/s

→ Time taken = 20s

To find:-

→ Power required by engine of the car

Solution:-

Firstly, let's calculate the acceleration of the car by using the 1st equation of motion :-

=> v = u + at

=> 20 = 0 + a(20)

=> 20 = 20a

=> a = 20/20

=> a = 1m/s²

Force developed :-

=> F = ma [ 2nd law of motion ]

=> F = 1000(1)

=> F = 1000 N

Now, let's calculate the distance travelled by the car using the 2nd equation of motion :-

=> s = ut + 1/2at²

=> s = 0(t) + 1/2×1×(20)²

=> s = 0 + 1/2×400

=> s = 200

Work done :-

=> W = F × s

=> W = 1000(200)

=> W = 200000 J

Hence, power :-

=> P = W/t

=> P = 200000/20

=> P = 10000 W

=> P = 10 kW

Thus, power required by the engine of the car is 10 kW [ Option.1 ] .

Answer 2

Answer:

$\bold{Power = 10kW}$

Explanation:

$\boxed{\bold{\large{Given :}}}$

✒ Mass = 1000 kg

✒ Initial Velocity (u) = 0 [When a body is in rest it's velocity is zero]

✒ Final Velocity (v) = 72km/h

• Let's change the final velocity to m/s.

72 × $\frac{5}{18}$ = 20 m/s

✒ Time = 20 s

$\boxed{\bold{\large{Knowledge\: \: Required :}}}$

You should know the three equations of motion

☘️ First Equation of Motion : v = u + at

☘️ Second Equation of Motion : s = ut + ½ at²

☘️ Third Equation of Motion : v² = u² + 2as

v → Final Velocity

u → Initial Velocity

a → Acceleration

s → Displacement

t → Time

Force = Mass × Acceleration

Work Done = Force × Displacement

Power = Work Done / Time

$\boxed{\bold{\large{To \: \: Find :}}}$

Power required by engine of the car

$\boxed{\bold{\large{Solution:}}}$

In order to find the Power required by engine of the car we need to find :-

♦ Acceleration

♦ Displacement

♦ Force

♦ Work Done

♦ Power

♦ Let's find the Acceleration (a) firstly.

v = u + at

⇒ 20 = 0 + (a × 20)

⇒ 20 = 20a

⇒ 20/20 = a

⇒ 1 m/s² = a

⇒ a = 1 m/s²

$\bold{Acceleration (a)\: = \: 1m/s^2}$

♦ Now let's find the Displacement (s).

v² = u² + 2as

⇒ 20² = 0² + (2 × 1 × s)

⇒ 400 = 0 + 2s

⇒ 400/2 = s

⇒ 200 m = s

⇒ s = 200 m

$\bold{Displacement (s) \: = 200m}$

♦ Now let's find the Force (F).

Force = Mass × Acceleration

Force = 1000 × 1

Force = 1000 N

$\bold{Force (F) \: = 1000N}$

♦ Now let's find the Work Done (W).

Work Done = Force × Displacement

Work Done = 1000 ×200

Work Done = 200000 J

$\bold{Work \: Done = 200000 J}$

♦ Now finally we will find the Power (P).

Power = Work Done / Time

Power = 200000 / 20

Power = 10000 W

Power = 10 kW

1000 W = 1 kW

$\bold{Power = 10kW}$

❤️ Happy Studying ! ☺️