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Question

The displacement-time equation for a particle in linear motion is given as x=ab(1−e−bt)). Which of the following options is/are correct?

A
The velocity and acceleration of the particle at t=0 is a and ab respectively.
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B
The velocity decreases as the time increases.
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C
The displacement of the particle lies between
0xab
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D
The maximum magnitude of acceleration during motion is ab
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Solution

The correct option is D The maximum magnitude of acceleration during motion is ab
x=ab(1ebt)Velocity v=dxdt=aebt Acceleration A=dvdt=abebt So, at t=0v=a and A=ab Also with time, velocity decreases. magnitude of maximum acceleration is ab. Now at t=0x=0 when tx=ab So, 0xab All the four options are correct.

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