Question

What is the work due to increase the velocity of a car from 18 km per hour to 90 km per hour, if the mass of the car is 2000 kg

Answer 1

Answer:

600kJ

Step by Step Explanation:

According to Work Energy Theorem,

Work Done = Change in Kinetic Energy ( Δ KE )

⇒ Final KE - Initial KE = Δ KE

Lets first convert all the velocities to m/s

1 km/hr = 0.27 m/s

⇒ 18 km/hr = 5 m/s

⇒ 90 km/hr = 25 m/s

Initial Velocity = 5 m/s

⇒ Initial KE = 1/2 mv²

⇒ Initial KE = 1/2 × 2000 kg × 5 × 5 = 25000 J

Final Velocity = 25 m/s

⇒ Final KE = 1/2 mV²

⇒ Final KE = 1/2 × 2000 × 25 × 25 = 625000 J

Δ KE = 625000 J - 25000 J

Δ KE = 6,00,000 J pr 600 kJ

Hence the work done to increase the velocity of the car is 600 kJ.

Hope it helped !!

Answer 2

$\sf{\huge{SOLUTION}}$ :

Given,

Mass of the car = 2000 kg
Initial velocity of the car, v₁ = 18 km/hr = 5 m/s
Final velocity of the car, v₂ = 90 km/hr = 25 m/s

Initial Kinetic Energy, K. E. ₁  = ½ × m × v₁²

K. E. ₁  = ½ × 2000 × 5²

K. E. ₁  = 25000 kg m²/s²

Final Kinetic Energy, K. E. ₂ = ½ × m × v₂²

K. E. ₂ = ½ × 2000 × 25²

K. E. ₂ = 625000 kg m²/s²

By Work - Energy Theorem,

The work done by constant force acting on a body is equal to the change produced in the kinetic energy.

W = ΔK = K. E. ₂ - K. E. ₁ 

W = ( 625000 - 25000 ) kg m²/ s²

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W = 600000 kg m²/ s²

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