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Question #43501

Difficulty: 8/10 | 🟢 Free

The Question

A car of mass $m$ starts from rest on a horizontal road. The car's engine delivers a constant power $P$ . The car experiences an aerodynamic drag force given by $F_d = kv^2$ , where $k$ is a positive constant and $v$ is the instantaneous velocity of the car. Which of the following expressions gives the distance $x$ covered by the car from its starting point to the point where it reaches a velocity $v_0 = \left(\frac{P}{2k}\right)^{1/3}$ ?

Options

A.
$\frac{m}{3k} \ln(2)$
B.
$\frac{m}{k} \ln(2)$
C.
$\frac{m}{6k}$
D.
$\frac{m}{2k} \ln\left(\frac{3}{2}\right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Power-Velocity Relationship|Non-Uniform Acceleration Constraint|Average vs. Instantaneous Calculus

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle non-linear, velocity-dependent forces under a constant power constraint.

A common trap is treating $P = Fv$ as a state equation to find an 'average' force or attempting to apply the Work-Energy Theorem ( $W = \Delta K$ ) using an incorrectly averaged net force over distance.

Because the drag force $F_d = kv^2$ makes the net work path-dependent in velocity space, students cannot bypass the differential equation $mv(dv/dx) = P/v - kv^2$ .

Those who ignore the drag force entirely will erroneously obtain $m/6k$ , while those who make integration errors by missing the chain rule factor of 3 will select $m/k \ln(2)$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Power-Velocity Relationship
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free