Statement - 1 - For a particle undergoing rectilinear motion with constant acceleration- the average velocity cannot be equal for two different time intervals- Statement -2 - The average velocity of particle moving with constant acceleration in a time interval is u-v2 - where u is the initial velocity and v is the final velocity- nbsp-Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1-Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1-Statement 1 is correct and statement 2 is incorrect-Statement 1 is incorrect and statement 2 is correct-

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Finding Average Velocity

Statement - 1...

Question

Statement - 1 : For a particle undergoing rectilinear motion with constant acceleration, the average velocity cannot be equal for two different time intervals.
Statement -2 : The average velocity of particle moving with constant acceleration in a time interval is $\frac{\to u + \to v}{2}$ ,
where $\to u$ is the initial velocity and $\to v$ is the final velocity.

Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.

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Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1.

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Statement 1 is correct and statement 2 is incorrect.

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Statement 1 is incorrect and statement 2 is correct.

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Solution

The correct option is D Statement 1 is incorrect and statement 2 is correct.
Average velocity of particle moving with constant acceleration in time interval $t = t_{1}$ to $t = t_{2}$ is equal to the average velocity in time interval $t = (t_{1} + Δ t)$ to $t = (t_{2} - Δ t)$ .
Let the initial velocity at time $t = 0$ be $u$
For interval $t = t_{1}$ to $t = t_{2}$
Velocity at time $t = t_{1}$ is given by
$v_{1} = u + a t_{1}$
Velocity at time $t = t_{2}$ is given by
$v_{2} = u + a t_{2}$
Average velocity in the time interval $t = t_{1}$ to $t = t_{2}$ is given by
$v_{a v g} = \frac{v_{1} + v_{2}}{2} = \frac{2 u + a (t_{1} + t_{2})}{2}$
For interval $t = t_{1} + Δ t$ to $t = t_{2} - Δ t$
Velocity at time $t = t_{1} + Δ t$ is given by
$v_{1}^{'} = u + a (t_{1} + Δ t)$
Velocity at time $t = t_{2} - Δ t$ is given by
$v_{2}^{'} = u + a (t_{2} - Δ t)$
Average velocity in the time interval $t = t_{1} + Δ t$ to $t = t_{2} - Δ t$ is given by
$v_{a v g} = \frac{v_{1}^{'} + v_{2}^{'}}{2} = \frac{u + a (t_{1} + Δ t) + u + a (t_{2} - Δ t)}{2} = \frac{2 u + a (t_{1} + t_{2})}{2}$
Hence , statement 1 is incorrect and statement 2 is correct

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Q. Statement - 1 : For a particle undergoing rectilinear motion with constant acceleration, the average velocity cannot be equal for two different time intervals.
Statement -2 : The average velocity of particle moving with constant acceleration in a time interval is

\frac{\to u + \to v}{2}

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\to u

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Statement 1-The graph between velocity v/s displacement of a praticle in a Rectilinear motion for which velocity is directly proportional to net force applied is a straight line

Statement 2- the velocity-displacement graph is straight line if slope of accelaration-time is zero.

A.Statement 1 and Statement 2 is true.Statement-2 is correct explanation for statement-1.

B.Statement 1 and Statement 2 is true.Statement-2 is not correct explanation for statement-1.

C.Statement 1 is false and Statement 2 is true.

D.Statement 1 is true and Statement 2 is false.

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