Question:
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard?s room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard?s room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
Updated On: Jul 5, 2022
- $\frac{u+v}{2}$
- $\frac{1}{2}\sqrt{u^{2}+v^{2}}$
- $\sqrt{uv}$
- $\sqrt{\left(\frac{u^{2}+v^{2}}{2}\right)}$
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The Correct Option is D
Solution and Explanation
Let $'S'$ be the distance between two ends $'a'$ be the constant acceleration
As we know $V^2 - u^2 = 2aS$
or, $aS=\frac{V^{2}-u^{2}}{2}$
Let $V$ be velocity at mid point.
Therefore, $V^{2}_{c}-u^{2}=2a \frac{S}{2}$
$V^{2}_{c}=u^{2}+aS$
$V^{2}_{c}=u^{2}+\frac{V^{2}-u^{2}}{2}$
$V_{c}=\sqrt{\frac{u^{2}+v^{2}}{2}}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.