Solved Examples on Displacement Formula

Question 1: Find the displacement covered by an object which accelerates from rest to 60 m/s in 3s. 

Solution: Initial velocity = 0 and final velocity = 60 m/s.

Time taken = 3s. 

Therefore, acceleration = 60/3 = 20m/s².

Displacement (S) = ut + ½ at² 

                             = 90 m

Question 2: Find the displacement of an object if it moves with an acceleration of 4 m/s² for 5s, where the initial velocity was 2 m/s.

Solution: Given initial velocity = 2 m/s, acceleration a  = 4 m/s² , and t =  5s, so the displacement will be:

Displacement =

v2−u22a�2−�22�

Also, we know that

a=v−ut�=�−�� => 4 =

v−25�−25 =>   v = 22

S=(22)2−(2)22×4=484−48=60m�=(22)2−(2)22×4=484−48=60�

Question 3:  A Person’s office is 5 m to the west and 4m south of his house.  He wants to take the shortest distance. Determine the shortest distance he covered to reach his office early.

Solution: The shortest distance can be determined by using the pythagoras formula:

(5)2+(4)2−−−−−−−−−√=25+16−−−−−−√=41−−√(5)2+(4)2=25+16=41 ~ 6.44 m

Question 4: Mithila throws the cricket ball 30 feet east for her pet. Her pet catches the ball and takes it past you, and you are standing 38 feet to the west of where Mithila is. What is the displacement of the cricket ball?

Solution: Initial position = 0 km and the final position is calculated by 38 − 30 = − 8 km

Now, using the formula, Δx  = x_f − x_i = − 8 − 0 = − 8 m

D = 8 m of Mithila’s initial position.