A particle starting from rest is subjected to a constant force. The plot of distance traveled along thedirection of the force as a function of time is a/an ______.a)straight lineb)circlec)parabolad)ellipseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

**Explanation:**

When a particle is subjected to a constant force, its distance traveled along the direction of the force as a function of time can be represented by a parabolic plot.

**1. Motion under Constant Force:**
When a particle is subjected to a constant force, it undergoes accelerated motion. The acceleration of the particle is given by Newton's second law of motion:

F = ma

where F is the force acting on the particle, m is the mass of the particle, and a is the acceleration of the particle.

**2. Distance as a Function of Time:**
The distance traveled by the particle along the direction of the force can be determined by integrating the velocity of the particle with respect to time:

s = ∫v dt

where s is the distance traveled, v is the velocity of the particle, and t is the time.

**3. Relationship between Velocity and Time:**
The velocity of the particle can be determined by integrating the acceleration of the particle with respect to time:

v = ∫a dt

Substituting the value of acceleration from Newton's second law of motion, we get:

v = ∫(F/m) dt

**4. Relationship between Distance and Time:**
Substituting the value of velocity in the equation for distance, we get:

s = ∫(∫(F/m) dt) dt

Simplifying the equation, we get:

s = (1/2)(F/m)t^2

This equation represents a parabolic plot of distance traveled along the direction of the force as a function of time. Hence, the correct answer is option 'C' - parabola.

Answer

Because unstable , unbounded motion.

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