When a 2 kg car moving at 20 m s⁻¹ coasts freely its velocity follows v = 20/(1 + t/20) m s⁻¹. Find power required to maintain 10 m s⁻¹ on same road (W).
Physics · Mixed Chapter
JEE Main Practice

Question

When a 2 kg car moving at 20 m s⁻¹ coasts freely its velocity follows v = 20/(1 + t/20) m s⁻¹. Find power required to maintain 10 m s⁻¹ on same road (W).

G1 Physics · Accepted Answer

Step 1 — Coasting deceleration determines resistive force: Fᵣ = −m dv/dt. Step 2 — The printed velocity law is v(t) = 20/(1+t/20); differentiate carefully to obtain dv/dt = −1/(1+t/20)². Step 3 — At v = 10, 1+t/20 = 2 and deceleration magnitude is 1/4 m s⁻². Then resistive force Fᵣ = 2 × 1/4 = 0.5 N. Step 4 — Required steady power P = Fᵣv = 0.5 × 10 = 5 W.