The two ends of train moving with constant acceleration pass a certain point with velocities u and 2 u. The velocity with which, the middle point of the train passes the same points is.

Question

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Answer 1

Hint: Apply kinematical equations.
Correct Option: Option A

Explanation for correct answer:

Step 1: Find the length of train in terms of velocity and acceleration.

The displacement of the train is given by:
$S = \frac{v ^{2} - u ^{2}}{2 a}$ , where $v$ and $u$ are the initial and final velocities of the train and $a$ is the acceleration of the train
If $L$ is the length of the train, then:

$L = \frac{( 2 u ) ^{2} + u ^{2}}{2 a} = \frac{3 u ^{2}}{2 a}$ ------(1)

Step 2: Find the velocity of midpoint.

As, midpoint is at distance $\frac{L}{2}$ ,

$\frac{L}{2} = \frac{v ^{2} - u ^{2}}{2 a}$

$\Rightarrow \frac{3 u ^{2}}{4 a} = \frac{v ^{2} - u ^{2}}{2 a}$

$\Rightarrow v = 2.5 u$ $m / s$

So, the velocity with which, the middle point of the train passes the same point is $2.5 u$ $m / s$ .

Answer 2

Hint: Apply kinematical equations.

Correct Option: Option A

Explanation for correct answer:

Step 1: Find the length of train in terms of velocity and acceleration.

The displacement of the train is given by:

S = \frac{v ^{2} - u ^{2}}{2 a}

, where

v

and

u

are the initial and final velocities of the train and

a

is the acceleration of the train

If $L$ is the length of the train, then:

$L = \frac{( 2 u ) ^{2} + u ^{2}}{2 a} = \frac{3 u ^{2}}{2 a}$ ------(1)

Step 2: Find the velocity of midpoint.

As, midpoint is at distance $\frac{L}{2}$ ,

$\frac{L}{2} = \frac{v ^{2} - u ^{2}}{2 a}$

$\Rightarrow \frac{3 u ^{2}}{4 a} = \frac{v ^{2} - u ^{2}}{2 a}$

$\Rightarrow v = 2.5 u$ $m / s$

So, the velocity with which, the middle point of the train passes the same point is $2.5 u$ $m / s$ .

The two ends of train moving with constant acceleration pass a certain point with velocities u and 2 u. The velocity with which, the middle point of the train passes the same points is.

$2.5 u$

$1.5 u$

$5 u$

u

The engine of a train passes an electric pole with a velocity $^{'} u^{'}$ and the last compartment of the train crosses the same pole with a velocity $v$ . Then find the velocity with which the mid-point of the train passes the pole. Assume acceleration to be uniform.

A car moving with a constant acceleration covers the distance between two points $180 m$ apart in $6 s$ . If its speed as it passes the second point is $45 m s^{- 1}$ , its speed at the first point is

A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passes the second point was 15.0 m/s. What is the acceleration?

A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passes the second point was 15.0 m/s.What was the speed at the first point?

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The two ends of train moving with constant acceleration pass a certain point with velocities u and 2 u. The velocity with which, the middle point of the train passes the same points is.

2.5​u

1.5​u

5​u

u

The engine of a train passes an electric pole with a velocity ′u′ and the last compartment of the train crosses the same pole with a velocity v. Then find the velocity with which the mid-point of the train passes the pole. Assume acceleration to be uniform.

A car moving with a constant acceleration covers the distance between two points 180m apart in 6s. If its speed as it passes the second point is 45ms−1, its speed at the first point is

A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passes the second point was 15.0 m/s. What is the acceleration?

A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passes the second point was 15.0 m/s.What was the speed at the first point?

Revise with Concepts

Velocity - Time Relation in Uniform Accelerated Motion

Position - Time Relation in Uniform Accelerated Motion

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$2.5 u$

$1.5 u$

$5 u$

The engine of a train passes an electric pole with a velocity $^{'} u^{'}$ and the last compartment of the train crosses the same pole with a velocity $v$ . Then find the velocity with which the mid-point of the train passes the pole. Assume acceleration to be uniform.

A car moving with a constant acceleration covers the distance between two points $180 m$ apart in $6 s$ . If its speed as it passes the second point is $45 m s^{- 1}$ , its speed at the first point is