Question

A particle of 10kg is moving in a constant acceleration 2m/s² starting from rest what is its momentum and velocity with time of 2.5sec​

Answer 1

Answer :

›»› The momentum of a particle is 50 kg·m/s.

›»› The velocity of a particle is 5 m/s.

Explanation :

Given :

• Mass of a particle = 10 kg.
• Acceleration of a particle = 2 m/s².
• Initial velocity of particle = 0 m/s.
• Time taken by particle = 2.5 sec.

To calculate :

• Momentum of particle = ?
• Velocity of particle = ?

Formula required :

Formula to calculate the velocity of a particle is given by,

→ v = u + at.

This formula is known as first equation of motion.

Here,

• v is the final velocity.
• u is the initial velocity.
• a is the acceleration.
• t is the time taken.

Units,

• The unit of final velocity is m/s.
• The unit of initial velocity is m/s.
• The unit of acceleration is m/s².
• The unit of time taken is second.

Formula to calculate the momentum of a particle is given by,

→ p = mv.

Here,

• p is the momentum.
• m is the mass.
• v is the final velocity.

Units,

• The unit of momentum is kg·m/s
• The unit of mass is kg.
• The unit of final velocity is m/s.

Calculation :

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

→ v = u + at.

By using the first equation of motion to calculate the velocity of a particle and substituting all the given values in the formula, we get :

→ v = 0 + 2 × 2.5

→ v = 0 + 5

→ v = 5.

Hence, the velocity of a particle is 5 m/s.

Now,

We know that, if we are given with the mass of a particle and final velocity of a particle then we have the required formula, that is,

→ p = mv.

By using the formula to calculate the momentum of a particle and substituting the given values in the formula, we get :

→ p = 10 × 5.

→ p = 50.

Hence, the moment of a particle is 50 kg·m/s.

Answer 2

Answer:

Given :-

• A particle of 10 kg is moving in a constant acceleration of 2 m/s² starting from rest and time of 2.5 seconds.

To Find :-

• What is the momentum and velocity.

Formula Used :-

❶ To find velocity we know that,

★ v = u + at ★

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

❷ To find momentum we know that,

✪ Momentum = Mass × Velocity ✪

Solution :-

Given :

• Mass = 10 kg
• Initial velocity = 0 m/s
• Acceleration = 2 m/s²
• Time = 2.5 seconds

❶ To find velocity,

Given :

• Initial velocity = 0 m/s
• Acceleration = 2 m/s²
• Time = 2.5 seconds

According to the question by using the formula we get,

↦ v = 0 + 2(2.5)

↦ v = 0 + 5

➦ v = 5 m/s

∴ The velocity of a particle is 5 m/s .

❷ To find momentum,

Given :

• Mass = 10 kg
• Velocity = 5 m/s

According to the question by using the formula we get,

⇒ Momentum = 10 kg × 5 m/s

➠ Momentum = 50 kg m/s

∴ The momentum of a particle is 50 kg m/s .