Solved Examples on Equations of Motion

Example 1: Mahesh throws the ball in the horizontal direction. If the ball travels 60 meters in 4 seconds they calculate the acceleration.

Solution: 

As the body is thrown that means the initial velocity is zero.

⇒ u = 0

The distance traveled by the ball is displacement.

⇒ s = 80 meters

The time period is t = 4 s.

By using the equation, s = ut + at²/2

⇒ 80 = 0(4) + a(4)²/2

⇒ 80 = 8a

⇒ a=10 m/s²

Therefore the acceleration of the body after is 10 m/s².

Example 2: A body is moving with a constant acceleration of 10 m/s². If the initial velocity of the body is 5 m/s then what will be its velocity after 2 seconds?

Solution:

The acceleration of the body is 10 m/s²

⇒ a = 10 m/s²

The initial velocity is 5 m/s.

⇒  u = 5 m/s

The time period is 2 sec.

⇒ t = 2 sec

By using the equation, v = u + at

⇒ v = 5 + 10(2)

⇒ v = 5  + 20

⇒ v = 25 m/s

Therefore the velocity of the body after 2 seconds is 25 m/s.

Example 3: A body is moving with a constant acceleration of 10 m/s². If the initial velocity of the body is 5 m/s and the final velocity is 105 m/s then what will be its displacement?

Solution:

The acceleration of the body is 10 m/s².

⇒ a = 10

The initial velocity is 5 m/s.

⇒ u = 5 m/s

The final velocity is 105 m/s.

⇒ v = 105 m/s

By using the equation, v² – u² = 2as

⇒ 105² – 5² = 2(10)(s)

⇒  s = (11025 – 25)/20

⇒  s = 550 sec

Therefore the time period is 550 seconds.

Example 4: What will be the displacement of a body if the initial and final velocities are 20 and 70 m/s respectively in 5 seconds?

Solution:  

The initial velocity is 20 m/s.

⇒ u = 20 m/s

The final velocity is 170 m/s.

⇒ v = 70 m/s

The time period is 5 sec.

⇒  t = 5 sec

By using the equation, s = (1/2) (v + u)t

⇒ s = (0.5) (70 + 20)(5)

⇒ s = 550 meters

Therefore the displacement of a body is 550 meters.

Example 5: A car is moving with a velocity of 50 m/s when the driver sees a person crossing the road applies brakes and the car stops after 4 seconds. Calculate the distance traveled by car.

Solution:

The initial velocity is 50 m/s.

⇒ u = 50 m/s

The final velocity is 0 m/s.

⇒ v = 0 m/s

The time period is 4 seconds.

⇒ t = 4s

By using the equation, s = (1/2)(v + u)t

⇒ s = (0.5)(50 + 0)(4)

⇒ s = 100 meters

Therefore the displacement of the body is 100 m.

Example 6: A car is decelerating at 6m/s². What is the distance traveled by the car if the initial speed is 20 m/s and the time taken to stop the car is 3 seconds?

Solution:

The deceleration of the body is 6 m/s²

⇒ a = 6

The initial velocity is 20 m/s.

⇒ u= 20 m/s

The time period is 3 sec.

⇒ t = 3 sec

By using the equation, s = ut – at²/2

⇒ s = 20(3) + 6(3)²/2

⇒ s = 60+27

⇒ s = 87 m

Therefore the displacement of the body is 87 m.

Equations of Motion was given by Sir Issac Newton; who is considered the father of mechanics. He was the first to give the fundamental physical laws that deal with objects and their motion. He formulated three equations of motion of an object and published them in his book Philosophiae Naturalis Principia Mathematica, which is considered the starting point in the history of classical mechanics.