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 x a

= 1000 kg x 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 x a

= 50 kg x 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 x a

= 100 kg x 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 ,

F=m×a

⇒10N=m×2m/s2

⇒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×a

1000N=m×5 m/s2

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×a

50000 N=m×10m/s2