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Matter In Our Surroundings

Question
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A body moves from rest from a point A. It moves to another point B in 10 s, the motion being accelerated one and achieves a velocity 60 m/s at B. It then moves on to C with the uniform velocity for 20 s when it is immediately brought to rest. Draw a graph showing the complete motion and calculate the total distance travelled.

Solution

Given, a body from rest.


The above figure illustrates the motion of body at different points.
AB represents the accelerated part of motion.
BC represents the uniform motion.
At C, velocity of the body is abruptly made zero (point Q).

Distance travelled during the first 10 s is, 
equals space space space Area space of space increment ABP
equals space 1 half cross times space AP space cross times space BP space
equals space 1 half cross times 10 cross times 60
equals space 300 space straight m
Distance space travelled space during space the space next space 20 space straight s space is space given space by comma space

space Area space of space rectangle space PBCQ space equals space 20 space cross times space 60 space equals space 1200 space straight m

therefore space space space Total space distance space travelled space equals space 300 space plus 1200
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1500 space straight m