prove that if a body is thrown vertically upward , the time of ascent is equal to the time of descent.

Ascent:

Time of ascent be t seconds and the object be thrown with an initial velocity be u m/s.

Descent:

Time of descent be t' seconds and the object final velocity be v m/s. The distance covered will be the same as when the object is thrown upwards.

From equation (1) and (2) we can see that u = v. 

t' = t, that is, time of ascent is equal to time of descent.

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