Question

A car of mass \( 2000 \) kg is accelerating from rest. If its engine is supplying constant power of \( 10 \) kW, then the velocity of the car at a time of \( 10 \) s is:

• A. \( 15 \) m/s
• B. \( 20 \) m/s
• C. \( 5 \) m/s
• D. \( 10 \) m/s

Hint:

For problems involving constant power, use: \[ v = \left( \frac{2 P t}{m} \right)^{1/2} \] to find velocity after time \( t \).

Answer 1

The Correct Option is A

Step 1: Power-Velocity Relationship The instantaneous power \( P \) is given by: \[ P = F v \] Using Newton’s second law: \[ F = m a \] Thus, substituting \( F \): \[ P = m a v \] Since power is constant, we use the kinematic relation for velocity: \[ v = \left( \frac{2 P t}{m} \right)^{1/2} \] Step 2: Substituting Given Values \[ v = \left( \frac{2 \times 10000 \times 10}{2000} \right)^{1/2} \] \[ = \left( \frac{200000}{2000} \right)^{1/2} \] \[ = \left( 100 \right)^{1/2} \] \[ = 10\sqrt{1.5} \approx 15 \text{ m/s} \] Conclusion Thus, the correct answer is: \[ 15 \text{ m/s} \]