# Force and Laws of Motion

## Newton's Second Law of Motion

### Numerical Problems Based on Newton's Second Law of Motion - 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 questions:

Acceleration (a) = 5m/s2 and Mass (m) = 1000 kg, therefore, Force (F) =?

We know that, F = m x a

����������������������������= 1000 kg x 5m/s2

����������������������������= 5000 kg m/s2

Therefore, required Force = 5000 m/s2 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 x a

����������������������������= 50 kg x 2m/s2

����������������������������= 100 kg m/s2

Therefore, required Force = 100 m/s2 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/s2 and Mass (m) = 100 kg, therefore, Force (F) =?

We know that, F = m x a

= 100 kg x 3m/s2

= 300 kg m/s2

Therefore, required Force = 300 m/s2 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 x a 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 x a 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 x a 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

Therefore, Thus acceleration of the vehicle = 5 ms-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

Therefore, Thus acceleration of the vehicle = 0.5 ms-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

Therefore, Thus acceleration of the vehicle = 0.2 ms-2

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