A force applied by the engine of a train of mass 2 × 10⁶ kg changes its velocity from 10 m s⁻¹ to 20 m s⁻¹ in 10 minutes. The average power of the engine is ______ MW.
Physics · Mixed Chapter
JEE Main Practice

Question

A force applied by the engine of a train of mass 2 × 10⁶ kg changes its velocity from 10 m s⁻¹ to 20 m s⁻¹ in 10 minutes. The average power of the engine is ______ MW.

G1 Physics · Accepted Answer

Step 1: m = 2 × 10⁶ kg; u = 10 m s⁻¹; v = 20 m s⁻¹; Δt = 10 × 60 = 600 s. Step 2: Assuming the engine's work equals the change in kinetic energy, ΔK = ½m(v² − u²). Step 3: ΔK = ½ × (2 × 10⁶) × (400 − 100) = 3 × 10⁸ J. Step 4: Average power P̄ = ΔK/Δt = (3 × 10⁸)/600 = 5 × 10⁵ W = 0.5 MW. Final answer: 0.5 MW.