Question

Two trains A and B of length 400 m each are moving on two parallel tracks with uniform speed of

20 m/s in the same direction. with A ahead of B, driver of B accelerates at $1m/s^2$ in order to overtrake. if after 50 sec, the guard of B just brushes past driver of A, what was original distance between drivers of the trains?

• A. $450m$
• B. $1250m$
• C. $850m$
• D. $1650m$

Answer 1

The correct option is C $850m$

The relative speed of $B$ wrt $A$ will be $V_{BA}=V_B-V_A=20-20=0$

their relative acceleration will be $a_{BA}=a_B-a_A=1-0=1m/s^2$

the distance traveled will be in $s=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}1\times (50{)}^2=1250meter$

if initial separation was $x$ then $x+400m=s$ or $x=1250-400=850m$

because now the drivers are side by side of each other so the length of train A was added.