# 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

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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/s2 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/s2, 10 N force is required. Find the mass of object.

Solution: According to the question:

Acceleration (a) = 2m/s2, 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/s2, what will be the weight of the object?

Solution: According to the question,

Acceleration (a) = 2m/s2, 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/s2 after the applying of force equal to 50000 N. Find the mass of the vehicle.

Solution: According to the question,

Acceleration (a) = 10 m/s2, 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)