Question:
Two trains $A$ and $B$ each of length $400 \,m$ are moving on two parallel tracks with a uniform speed $72\, km\, h^{-1}$ in the same direction with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1\, m \,s^{-2}$. If after $50\, s$, the guard of $B$ just brushes past $A$, what was the original distance between them ?
Two trains $A$ and $B$ each of length $400 \,m$ are moving on two parallel tracks with a uniform speed $72\, km\, h^{-1}$ in the same direction with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1\, m \,s^{-2}$. If after $50\, s$, the guard of $B$ just brushes past $A$, what was the original distance between them ?
Updated On: Jun 14, 2022
- $750\,m$
- $1000\,m$
- $1250\,m$
- $2250\,m$
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The Correct Option is C
Solution and Explanation
For train $A$,
$u_{A}=72\,km\,h^{-1}=72\times\frac{5}{18}\,m\,s^{-1}=20\,m\,s^{-1}$, $a_{A}=0$, $t=50\,s$
$\therefore S_{A}=u_{A}\,t=\left(20\right)\left(50\right)=1000\,m$
For train $B$,
$u_{B}=72\,km\,h^{-1}=72\times\frac{5}{18}\,m\,s^{-1}=20\,m\,s^{-1}$
$a_{B}=\,m\,s^{-2}$, $t=50\,s$
$\therefore S_{B}=u_{B}t+\frac{1}{2}\,a_{B}t^{2}$
$=\left(20\times50\right)+\frac{1}{2}\times1\times\left(50\right)^{2}$
$=2250\,m$
Original distance between $A$ and $B = S_B - S_A$
$= 2250\, m - 1000 \,m = 1250 \,m$
$u_{A}=72\,km\,h^{-1}=72\times\frac{5}{18}\,m\,s^{-1}=20\,m\,s^{-1}$, $a_{A}=0$, $t=50\,s$
$\therefore S_{A}=u_{A}\,t=\left(20\right)\left(50\right)=1000\,m$
For train $B$,
$u_{B}=72\,km\,h^{-1}=72\times\frac{5}{18}\,m\,s^{-1}=20\,m\,s^{-1}$
$a_{B}=\,m\,s^{-2}$, $t=50\,s$
$\therefore S_{B}=u_{B}t+\frac{1}{2}\,a_{B}t^{2}$
$=\left(20\times50\right)+\frac{1}{2}\times1\times\left(50\right)^{2}$
$=2250\,m$
Original distance between $A$ and $B = S_B - S_A$
$= 2250\, m - 1000 \,m = 1250 \,m$
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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.