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Question

A particle moves in a straight line with the velocity as shown in the figure. At t=0,x=16 m, then,

A
The maximum value of the position coordinate of the particle is 54 m
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B
The maximum value of the position coordination of the particle is 36 m
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C
The particle is at the position of 36 m at t=18 s
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D
The particle is at the position of 36 m at t=30 s
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Solution

The correct options are
A The maximum value of the position coordinate of the particle is 54 m
C The particle is at the position of 36 m at t=18 s
D The particle is at the position of 36 m at t=30 s
Maximum value of position coordinate = initial coordinate + area under the graph upto t=24 s (As upto t=24 s, the displacement of the particle will be positive )
xmax=16+[(2×10)+(2+62)×(1810)+1×62×(2418)]
=16+[20+32+18]=54 m

At time t=18 s
xt=18=16+Area of graph upto t=18 s
xt=18=16+[20+32]=36 m

At time t=30 s
xt=30=16+Area of graph upto t=30 s
xt=30=16+[7012×6×6]=36 m

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