## Displacement Formula

Everything you need to know about the Displacement Formula is given below. Please continue reading the entire document carefully to fully understand the topic.

Displacement refers to the change of an object’s location from its original position to its final position. Moreover, it is a vector value and as a result, it has both direction and magnitude. In addition, it does not have an S.I unit so we can measure it in meters, miles, yards, feet, etc.

For example, if an object moves from the original position to the last position, then the position of the object changes. This change in the location of an object is called displacement.

## Formula

The displacement is calculated as:

**S = S _{f} – S_{i} **

where,

S = displacement

S_{f} = final position

S_{i} = initial position

OR

**S = ut + ½ at ^{2}**

where,

S = displacement

u = initial velocity

a = acceleration

t = time

Hence, displacement (s) of an object is equal to initial velocity(u) times time (t), plus half of the acceleration (½ a) multiplied by time squared (t2).

## Solved examples

**1. Suppose Radha travelled from Mumbai to Delhi to visit Meena. So, she travelled by train and, for the first time, travelled 350 kilometres north. However, the track goes back south 125 miles. Calculate Radha’s displacement rate using a displacement formula?**

**Solution:** Radha’s first position is S𝑖 = 0 and his last position Sf is the distance he travelled to the north minus the distance she travelled south. So, now enter the values in the equations.

S = S_{f} – S_{i}

S = (350 Km N – 125 Km S)

S = 225 Km N

Thus, the total displacement is 225 Km North of Radha.

**2. A car travelling at 25 m/s starts accelerating at 3 m/s ^{2} in 4 seconds. How far does a car travel in 4 fast seconds?**

**Solution:** The three required range variables are given u (25 m/s), a (3 m/s^{2}), and t (4 sec).

Put the values in the displacement formula;

S = ut + ½ at^{2}

S = 25 m/s * 4 sec + ½ * 3 m/s^{2} * (4 sec)^{2}

S = 124 meters

**3. It takes a plane, with an initial speed of 40 m/s, 13 seconds to reach the end of the runway. If the plane is travelling at 10 m/s ^{2}, how long is the flight path?**

**Solution:** The initial speed of the plane = 40 m/s

Time required to reach the end of the runway = 13 sec

Acceleration = 10 m/s^{2}

Substitute the given values in the displacement formula;

S = ut + ½ at^{2}

S = 40 m/s * 13sec + ½ * 10 m/s^{2} * (13 sec)^{2}

S = 1365 meters