Close to the Earth’s surface, a falling object experiences a constant downward acceleration of approximately 9.81 ms^{-2}. If we assume air resistance to be negligible, we can use the equations of motion for an object experiencing a constant acceleration to analyse the kinematics of the particle. Furthermore, to make matters simple, we will assume that the particle is moving along a line.

When doing typical calculations of this type, it is important to define a direction to be *positive*. Then, all vector quantities which point along this direction should be taken to be positive while quantities that point in the opposite direction should be taken to be negative.

## How to Find Velocity of a Falling Object, which Started from Rest

For this case, we have . Then, our four equations of motion become:

**Example**

*A stone is dropped from the Sydney Harbour Bridge, which is 49 m above the surface of water. Find the velocity of the stone as it hits the water.*

At the beginning, the stone’s velocity is 0. Taking the *downwards* direction to be positive, we have 49 m and 9.81 m s^{-2}. Using the fourth equation above, then, we have: m s^{-1}.

## How to Find Velocity of a Falling Object, which Did not Start from Rest

Here, the equations of motion apply as usual.

**Example**

*A stone is thrown downward at a speed of 4.0 m s ^{-1} from the top of a 5 m building. Calculate the speed of the stone as it hits the ground.*

Here, we use the equation . Then, . If we take downwards direction to be positive, then we have 4.0 m s^{-1}. and 9.81 m s^{-2}. Substituting the values, we get: m s^{-1}.

**Example**

*A stone is thrown upward at a speed of 4.0 m s ^{-1} from the top of a 5 m building. Calculate the speed of the stone as it hits the ground.*

Here, the quantities are the same as those in the previous example. The displacement of the body is still 5 m s^{-1} downwards, as the initial and final positions of the stone are the same as those in the earlier example. The only difference here is that the initial velocity of the stone is *upward*. If we take downward direction to be positive, then we would have -4 m s^{-1}. However, for this particular case, since , the answer should be the same as before, because squaring gives the same result as squaring .

**Example**

*A ball is thrown upwards at a speed of 5.3 m s ^{-1}. Find the velocity of the ball 0.10 s after it was thrown.*

Here, we’ll take upwards direction to be positive. Then, 5.3 m s^{-1}. The acceleration is downward, so -9.81 m s^{-2 } and time 0.10 s. Taking the equation , we have 4.3 m s^{-1}. Since we get a positive answer, this means that the ball is still travelling upward.

Let’s now try to find the velocity of the ball 0.70 s after it was thrown. Now, we have: -1.6 m s^{-1}. Note that the answer is negative. This means that the ball has reached the top, and is now moving down.