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Question #42037

Difficulty: 8/10 | 🟢 Free

The Question

A vehicle of mass $m = 1000 \text{ kg}$ is moving at $v_0 = 20 \text{ m/s}$ on a rough horizontal road, experiencing a constant braking friction force of $f = 8 \text{ kN}$ . At $t=0$ , it collides with a flexible barrier. The barrier exerts a constant retarding force of $F = 40 \text{ kN}$ on the vehicle for a duration of $\Delta t = 0.2 \text{ s}$ , after which the vehicle loses contact with the barrier. What is the work done by the barrier on the vehicle during the collision?

Options

A.
$-121.6 \text{ kJ}$
B.
$-128.0 \text{ kJ}$
C.
$-145.92 \text{ kJ}$
D.
$-160.0 \text{ kJ}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Stopping Distance Paradox|Collision Impulses|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between the total work done on a system and the work done by a specific non-conservative force during a finite-duration collision.

A common trap is to treat the collision as instantaneous and ignore the non-impulsive braking force, leading to an incorrect displacement and work ( $-128.0 \text{ kJ}$ ).

Another trap is correctly finding the final velocity but incorrectly attributing the entire change in kinetic energy to the barrier via a misapplied Work-Energy Theorem ( $-145.92 \text{ kJ}$ ).

Students must rigorously apply Newton's laws to find the true kinematic displacement during the impulse phase and isolate the barrier's work.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Stopping Distance Paradox
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free