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

Upward motion

v = u – gt₁

0 = u – gt₁

t₁ = {𝑢 \over 𝑔}              … (1)

Downward motion

v = u + gt₂

v = 0 + gt₂

As the body falls back to the earth with the same velocity it was thrown vertically upwards.

∴ v = u

v = 0 + gt₂

t2 = {𝑢 \over 𝑔}                … (2)

From (1) and (2), we get t₁ = t₂

⟹ Time of ascent = Time of descent