Question

A train moves from one station to another in $2$ hours time, its speed during the motion is shown in graph above. The maximum acceleration during the journey and distance covered during the time interval from $0.75$ hour to $1.00$ hour are

• A. $60km{hr}^{-2},100km$
• B. $160km{hr}^{-2},10km$
• C. $10km{hr}^{-2},10km$
• D. $260km{hr}^{-2},1km$

Answer 1

The correct option is B $160km{hr}^{-2},10km$

Maximum acceleration will occur in the region with maximum slope.
From the given curve region CD is having the maximum curve.
Thus, maximum acceleration$=\frac{changeinvelocity}{changeindistance}=\frac{60-20}{0.25}=160$
Now, total area under the curve between 0.75 to 1.00 hrs is given by
$(\frac{1}{2}\times 0.25\times 40)+(20\times 0.25)=10km$