Q. 155.0( 3 Votes )

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

Answer :

Consider the motion described by x(t) = t^{2} – t +1/4.

Then velocity v(t) can be written as

Acceleration a(t) can be written as

We can clearly see that for all time instants less than 0.5 seconds, the required conditions i.e. x > 0, v < 0 and a > 0 are satisfied.

(Important note: To find such an equation we can do reverse calculation, like considering acceleration as a positive constant and then integrating to find velocity and displacement according to the given conditions.)

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PREVIOUSGive examples of a one-dimensional motion where(a) the particle moving along positive x-direction comes to rest periodically and moves forward(b) the particle moving along positive x-direction comes to rest periodically and moves backward.NEXTAn object falling through a fluid is observed to have acceleration given by a = g – bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?

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