# Numericals

## Newton's Second Law of Motion

### Numerical 1:

**Type 1:**

Question 1: Calculate the force needed to speed up a car with a rate of 5ms^{–2}, if the mass of the car is 1000 kg.

**Solution:** According to question:

Acceleration (a) `= 5m//s^2` and Mass (m) = 1000 kg, therefore, Force (F) =?

We know that, `F = m xx a`

`= 1000 kg xx 5m//s^2`

`= 5000 kg\ m//s^2`

Therefore, required Force `= 5000 m//s^2` or 5000 N

Question 2: If the mass of a moving object is 50 kg, what force will be required to speed up the object at a rate of 2ms^{–2}?

**Solution:** According to the question;

Acceleration (a) `= 2ms^-2` and Mass (m) = 50 kg, therefore, Force (F) =?

We know that, `F = m xx a`

`= 50 kg xx 2m//s^2`

`= 100 kg\ m//s^2`

Therefore, required Force `= 100 m//s^2` or 100 N

Question 3: To accelerate a vehicle to 3m/s^{2} what force will be needed if the mass of the vehicle is equal to 100 kg?

**Solution:** According to the question:

Acceleration (a) `= 3m//s^2` and Mass (m) = 100 kg, therefore, Force (F) =?

We know that, `F = m xx a`

`= 100 kg xx 3m//s^2`

`= 300 kg\ m//s^2`

Therefore, required Force `= 300 m//s^2` or 300 N

**Type II:**

Question 1: To accelerate an object to a rate of 2m/s^{2}, 10 N force is required. Find the mass of object.

**Solution:** According to the question:

Acceleration (a) = 2m/s^{2}, Force (F) = 10N, therefore, Mass (m) = ?

We know that, `F = m xx a`

`=>10N=mxx2m//s^2`

`=>m=10/2\ kg =5\ kg`

Thus, the mass of the object = 5 kg

Question 2: If 1000 N force is required to accelerate an object to the rate of 5m/s^{2}, what will be the weight of the object?

**Solution:** According to the question,

Acceleration (a) = 2m/s^{2}, Force (F) = 1000N, therefore, Mass (m) = ?

We know that, `F = m xx a`

`=>1000N=mxx5\ m//s^2`

`=>m=1000/5\ kg = 200\ kg`

Thus, the mass of the object = 200 kg

Question 3: A vehicle accelerate at the rate of 10m/s^{2} after the applying of force equal to 50000 N. Find the mass of the vehicle.

**Solution:** According to the question,

Acceleration (a) = 10 m/s^{2}, Force (F) = 50000N, therefore, Mass (m) = ?

We know that, `F = m xx a`

`=>50000\ N = m xx 10m//s^2`

`=>m=50000/10\ kg = 5000\ kg`

Thus, the mass of the vehicle = 5000 kg

**Type - III**

Question 1: What the acceleration a vehicle having 1000 kg of mass will get after applying a force of 5000N?

**Solution:** According to question:

Mass (m) = 1000 kg, Force (F) = 5000N, Acceleration (a) =?

We know that, Force = Mass x Acceleration or F = m x a

`:. 5000\ N= 1000\ kg xx a`

`=>a=(5000\ N)/(1000\ kg)`

`=>(5000\ kg\ ms^(-2))/(1000\ kg)=5m//s^(-2)`

Thus acceleration of the vehicle `=5m//s^(-2)`

Question 2: After applying a force of 1000 N an object of mass 2000 kg will achieve what acceleration?

**Solution:**

According to the question,

Mass (m) = 2000 kg, Force (F) = 1000N, Acceleration (a) =?

We know that, Force = Mass x Acceleration or F = m x a

`:. 1000\ N= 2000\ kg xx a`

`=>a=(1000\ N)/(2000\ kg)`

`=>(1000\ kg\ ms^(-2))/(2000\ kg)=0.5m//s^(-2)`

Thus acceleration of the vehicle `=0.5m//s^(-2)`

Question 3: An object requires the force of 100N to achieve the acceleration ‘a’. If the mass of the object is 500 kg what will be the value of ‘a’?

**Solution:** According to the question,

Mass (m) = 500 kg, Force (F) = 100N, Acceleration (a) =?

We know that, Force = Mass x Acceleration or F = m x a

`:. 100\ N= 500\ kg xx a`

`=>a=(100\ N)/(500\ kg)`

`=>(100\ kg\ ms^(-2))/(500\ kg)=0.2m//s^(-2)`

Thus acceleration of the vehicle `=0.2m//s^(-2)`