Question

Universal express travels at 150km per hour and it overtakes motor bike at 64 km per hour in 70seconds calculate the length of the universal express travel

Answer 1

Given :

The speed of the universal express = 150 km per hr

The speed of motorbike = 64 km per hr

The time taken by the universal express to overtake the motorbike = 70 sec

To Find :

What is the length of the universal express ?

Solution :

The speed of universal express relative to the motorbike will be :

$V_{EM}$= (150 - 64) km per hour

      = 86 $\frac{km}{h}$

Or ,$V_{EM}$= $86 \times \frac{5}{18 }$ $\frac{m}{sec}$

            = $\frac{215}{9}$ m per sec

Now the length of the universal express will be equal to the distance traveled by it relative to the motorbike to overcome it .

Since there is no acceleration, so we can apply :

$\farc{speed }= \frac{distance}{time}$

So, $V_{EM} = \frac{L}{t}$

Here , L is length of the universal express and t is time taken to overtake .

So , $\frac{215}{9 } =\frac{L}{70}$

Or, $L = \frac{215}{9} \times 70$

Or , L = 1672 .22 m

Hence , the length of the universal express is 1672.22 m .