Question

An express train-starts from one station. After 40 min it crosses a small station which is at a
distance of 30 km. Find the velocity of train (in m/s) when it crosses the station. (Assume the
train accelerates uniformly and has no scheduled halt at the small station)
1) 90m/s
2) 45m/s
3) 25m/s
4) 50m/s​

Answer 1

Answer:

answer is 25 m/s

Explanation:

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Answer 2

Answer:

An express train starts from one station. After 40 min it crosses a small station which is at a  distance of 30 km. The velocity of the train (in m/s) when it crosses the station is $25\ m/s$

The correct answer is option 3.

Explanation:

• We know,

        $Velocity = \frac{Distance}{time}$  

• Let V be the velocity, S be the distance and t be the time taken to cover the distance. Then,  

         $V = \frac{S}{t}$               ...(1)          

         or  

        $S = Vt$              ...(2)

• For uniformly accelerated motion,

        Average velocity, $V_{avg} = \frac{v+u}{2}$        ...(3)

       where u is the initial velocity and  v is the final velocity

Substitute the value of V in equation(2),

$S = ( \frac{v+u}{2})t$       ...(4)

Given,  

$S= 30\ km = 30,000m$

$t = 30\ min = 40\times 60 = 2400\ s$

$u = 0 m/s$

Equation (4) becomes,

$30,000 = ( \frac{v+0}{2})\times2400$

$30,000 = ( \frac{v}{2})\times2400$

$v = \frac{30000\times2}{2400} = 25\ m/s$