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  • Give example of a motion where x>0, v<0, a>0 at a particular instant.

Give example of a motion where x>0, v<0, a>0 at a particular instant.

Answers (1)

Let x(t) be the function of motion,

x(t) = A + Be^{-\gamma t} \; \; \; \; \; ........ (i)

Here, \gamma & A are constant & B is the amplitude.

At time t the displacement is x(t),

Here A>B \; and\; \gamma > 0

Thus, v(t)=\frac{dx(t)}{dt}

                   =0+(-\gamma )Be^{-\gamma t}

                   =-\gamma Be^{-\gamma t}

Now, a(t)=\frac{d}{dt[v(t)]}

                  =\frac{d}{dt}(-\gamma \; B\; exp^{-\gamma t})

                  =(\gamma B^{2}exp^{-\gamma t})

Thus, we get,

x > 0, i.e., x is always positive, since A>B

v<0, i.e., v is always negative, since v<0

& a>0, i.e., a is always positive.

The value of \gamma Be^{-\gamma t} varies from 0 to +\infty

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infoexpert22

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