The work done to increase the velocity of a 1500 kg car from 36 km/h to 72 km/h is

The correct option is: 2

Concept Used:

• Work-Energy Theorem: This theorem states that the net work done by the force on a body is equal to the change in its kinetic energy.
• Mathematically, Work Done (W) = Final Kinetic Energy - Initial Kinetic Energy
• Kinetic Energy (K.E) is given by the formula: K.E = (1/2) × m × v²
• So, W = (1/2) × m × (v² - u²), where:
  • m = mass of the object
  • v = final velocity
  • u = initial velocity

Calculation:

• Given:
  • Mass of the car (m) = 1500 kg
  • Initial velocity (u) = 36 km/h = 36 × (1000 ÷ 3600) = 10 m/s
  • Final velocity (v) = 72 km/h = 72 × (1000 ÷ 3600) = 20 m/s
• Using the work-energy theorem:
  W = (1/2) × m × (v² - u²)
  ⇒ W = (1/2) × 1500 × (20² - 10²)
  ⇒ W = (1/2) × 1500 × (400 - 100)
  ⇒ W = (1/2) × 1500 × 300
  ⇒ W = 750 × 300
  ⇒ W = 225000 J
  ⇒ W = 2.25 × 10⁵ J

Additional Information:

• Work done is a scalar quantity and is expressed in joules (J) in the SI system.
• This type of question is commonly asked in mechanics under the topic of energy and work.
• Always convert velocities from km/h to m/s before substituting in the kinetic energy formula: multiply by (1000 ÷ 3600) or simplify as 5/18.

Diagram/Visual Aid Suggestion:

• A diagram showing a car moving initially at a lower speed and then at a higher speed with vectors labeled u and v.
• Include a bar graph representing the initial and final kinetic energy for visual comparison.