Average Velocity in Straight Line Motion – Rankers Physics

Average Speed and Velocity: Practice Problem & Solution

Assertion (A): A particle moves in a straight line with constant acceleration. The average velocity of this particle can not be zero in any time interval. Reason (R): For a particle moving in straight line, the average velocity in a time interval is always ((frac{u+v}{2})), where (u) and (v) are initial and final velocities of the particle in given time interval.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Average Speed and Velocity. Understanding the underlying formula is key to arriving at the correct answer below:

Solution: (A) is false; average velocity can be zero if displacement is zero (e.g., object returns to start with constant acceleration). (R) is false; the formula \(v_{avg} = \frac{u+v}{2}\) is only valid for constant acceleration, not 'always' for any straight line motion.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Two particles are projected with same initial velocity one makes angle \(\theta\) with horizontal while other makes an angle \(\theta\) with vertical. If their common range is R then product of their time of flight is directly proportional to: (1999)
2. Assertion (A): If velocity of a particle moving in a straight line is zero at a point, its acceleration will be zero at that point. Reason (R): Wherever \(a = v \frac{dv}{dx}\) holds, \(v = 0 \Rightarrow a = 0\).  
3. Assertion (A): Trajectory of an object moving under a constant acceleration is a straight line. Reason (R): The shape of trajectory depends only on the acceleration.  
4. At what angle to the horizontal should an object be projected so that the maximum height reached is equal to the horizontal range?
5. Assertion (A): When the range of a projectile is maximum, the time of flight is the largest. Reason (R): Horizontal range is maximum when angle of projection is (90^circ).