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

Consider the motion described by x(t) = t2 – 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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