Question

A particle moves in straight line with initial velocity 6 m/s and accelerate uniformly

with 2 m/s2

find displacement in 5th second of its motion.​

Answer 1

Answer :

›»› The displacement of a particle in 5 second is 55 m.

Explanation :

Given :

• Initial velocity of partical = 6 m/s.
• Acceleration produced by particle = 2 m/s².
• Time taken by particle = 5 second.

To Find :

• Displacement of particle = ?

Formula required :

Formula to calculate the displacement of particle is given by,

→ s = ut + 1/2 at².

This is formula is known as second equation of motion.

Here,

• s is the Displacement of particle.
• u is the Initial velocity of particle.
• a is the Acceleration produced by particle.
• t is the Time taken by particle.

Units,

• The unit of Displacement is m.
• The unit of Initial velocity is m/s.
• The unit of Acceleration is m/s².
• The unit of Time taken is second.

Solution :

We know that, if we are given with the initial velocity of particle, acceleration produced by particle and time taken by particle then we have the required formula of second equation of motion, that is,

→ s = ut + 1/2 at².

By using the second equation of motion to calculate the displacement of particle and substituting all the given values in the equation, we get :

→ s = 6 * 5 + 1/2 * 2 * (5)²

→ s = 30 + 1/2 * 2 * (5)²

→ s = 30 + 1/2 * 2 * 25

→ s = 30 + 1 * 1 * 25

→ s = 30 + 1 * 25

→ s = 30 + 25

→ s = 55

Hence, the displacement of particle is 55 m.

Answer 2

Answer:

Given :-

• A particle moves in straight line with initial velocity 6 m/s and accelerates uniformly with 2 m/s² and its time taken is 5 seconds.

To Find :-

• What is the distance covered by the particle.

Formula Used :-

✧ s = ut + ½ at² ✧

where,

• s = Distance covered
• u = Initial velocity
• t = Time
• a = Acceleration

Solution :-

Given :

• Initial velocity = 6 m/s
• Acceleration = 2 m/s²
• Time = 5 seconds

According to the question by using the formula we get,

⇒ s = 6 × 5 + ½ × 2(5)²

⇒ s = 30 + ½ × 2 × 25

⇒ s = 30 + ½ × 50

⇒ s = 30 + 25

➠ s = 55 m

∴ The distance covered by the particle is 55 m .

★ Let's Verify :-

↦ s = ut + ½ at²

Put, s = 55

↦ 55 = 6 × 5 + ½ × 2(5)

↦ 55 = 30 + ½ × 2 × 25

↦ 55 = 30 + ½ × 50

↦ 55 = 30 + 25

↦ 55 = 55

➦ LHS = RHS

Hence, Verified ✔