A stone thrown vertically upwards with initial velocity u reaches a height h before coming down. Show that the time taken to go up is same as the time taken to come down.

Explanation

When object is thrown up
Initial velocity `=um//s`

Final velocity`=0m//s`
Acceleration`==gm//s^(2)`
Time taken to go up `=t_(1)`
According to 1st eq.of motion
`v=u+"gt"`
`0=u-"gt"_(1)`
`"gt"_(1)=u`
`t_(1)=u/g(s)`.....i
when object falls down.
Initial velocity `=0m//s`
Final velocity `(v)=um//s`
Acceleration `=gm//s^(2)`
Time taken to go down `=t_(2)`
According to 1st eq. of motion
`v=u+"gt"`
`u=0+"gt"_(2)`
`t_(2)=u/t(s)`.........ii
`t_(1)=t_(2)`