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Question

A particle starts its motion from x = 8 at t=0. The v−t graph of the particle is given in figure. The maximum x-coordinate of the particle is _____.

A
20
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B
180
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C
236
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D
188
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Solution

The correct option is C 236
The velocity of the particle is changing the sign at 24 sec. This means the particle is taking a U-turn at 24s. Therefore, the maximum X-coordinate can be observed at 24s. Displacement at 24s is the area under the graph from 0 to 24 s.
total area=(12.4.8)+(8×6)+12 6×(8+20)+128×20=228
x = 228
x - 8 = 228
x = 236

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