Question

Speed-time graph for the motion of the train is given in figure 16.1. What will be the acceleration of the train while accelerating

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Answer 1

RequirEd solution:

What will be the acceleration of the train while accelerating!?

ExplanaTion:

→ In a velocity-time or speed-time graph, the slope of graph tell us about the acceleration. If the slope is high then the acceleration is positive, if the solve is low then the acceleration is negative and if the slope is parallel to time axis then there is no acceleration taking place!

SoluTion:

~ Acceleration of car when acceleration in section AB is mentioned below:

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{10-0}{100-0} \\ \\ :\implies \sf a \: = \dfrac{10}{100} \\ \\ :\implies \sf a \: = \dfrac{1}{10} \\ \\ :\implies \sf a \: = 0.1 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 0.1 \: ms^{-2}$

~ Let's find out the acceleration in section CD too but here the train is retarding!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{0-10}{400-350} \\ \\ :\implies \sf a \: = \dfrac{-10}{50} \\ \\ :\implies \sf a \: = \dfrac{-1}{5} \\ \\ :\implies \sf a \: = -0.2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = -0.2 \: ms^{-2}$