Question

how to find intial velocity when you are given distance and acceleration? can you give an example and answer?

Answer 1

It's not possible to calculate initial velocity by only knowing distance and acceleration.

Because in each kinematics equation, there is five quantities. Initial velocity, final velocity, distance, time and acceleration. To calculate any quantity at least 3 quantity must be known.

v = u + at

In this equation by only knowing 'a' you can't calculate initial speed 'u'.

v^2 = u^2 + 2as

In this equation by only knowing 'a' and 's' you can't calculate initial speed 'u'.

s = ut + 1/2at^2

In this equation by only knowing 's' and 'a' you can't calculate initial speed 'u'.

So I am giving an example where final velocity, v = 0

This happens when you throw a ball in vertical direction with initial speed 'u' and the distance covered by ball upto maximum height, s = 10m.

In this case , acceleration which is gravitational acceleration acts in opposite direction to the motion means downward direction.

So a = - g = - 9.8m/s^2.

Now applying kinematic equation

v^2 = u^2 + 2as

0^2 = u^2 + 2*(-9.8)*10

u = √2*9.8*10

u = 14 m/s.