The change in momentum depends on the product of force and time.
Explanation
The scenario is governed by the concept of Impulse, which is derived from Newton's Second Law of Motion. Impulse quantifies the overall effect of a force acting over time and is equal to the change in momentum of an object.
Detailed Analysis
- Impulse-Momentum Theorem: The change in momentum ($\Delta p$) is equal to the product of the average force ($F$) applied and the time interval ($\Delta t$) during which the force acts:
Change in Momentum = Force × Time - Requirement for Starting: To push-start a vehicle with a dead battery, the vehicle must accelerate from rest to a sufficient velocity to engage the gears and turn the engine crankshaft. This requires a significant change in momentum.
- Sudden Jerk: A jerk implies a large force applied for a very short duration. Despite the high force, the minimal time interval results in a small product ($F \times \Delta t$), leading to a negligible change in momentum. The vehicle does not gain enough speed.
- Continuous Push: A continuous push applies force over a longer duration. Even if the force is moderate, the extended time interval significantly increases the product ($F \times \Delta t$), resulting in a large change in momentum. This allows the vehicle to attain the necessary velocity to start the engine.
Incorrect Options Analysis:
- The change in momentum is independent of the time duration.: Incorrect because the change in momentum is directly proportional to the time duration of the applied force.
- The static friction is less than the kinetic friction.: Incorrect because while static friction is greater than kinetic friction, this explains the initial resistance to motion, not the need for a sustained push to gain velocity.
- The engine requires a specific threshold of heat to ignite.: Incorrect because the immediate requirement is mechanical rotation (momentum), not heat generation.
Key Takeaway:
To achieve a significant change in momentum (velocity), a force must be applied over a sufficient period of time, as defined by the relationship Impulse = Force × Time.