Numerical Problems Based on Newton's Second Law of Motion(2) - Force & Laws of Motion - Class 9 PDF Download

Type - IV

Q.1. An object of 50 kg gets the speed of 10m/s in 5 second from zero velocity. Calculate the required force applied by engine of the car.
Ans.
According to the question:-
Initial velocity (u) = 0, final velocity (v) = 10m/s, time (t) = 5 second, Mass (m) = 50 kg,
Therefore, force (F) =?

⇒ 100kg ms^-2 ⇒ 100 N
Thus required force = 100 N

Q.2. A car having mass of 1500 kg achieve the velocity of 5 m/s in 10 second. Calculate the required force to attain required speed by car.
Ans.
According to the question:
Initial velocity (u) = 0, final velocity (v) = 5m/s, time (t) = 10 second, Mass (m) = 1500 kg,
Therefore, force (F) =?

⇒ 750 kgms^-2 or 750 N
Thus required force = 750 N

Q.3. A bus starts from the stop and take 50 second to get the speed of 10m/s. If the mass of the bus along with passengers is 10000 kg, calculate the force applied by the engine of bus to push the bus at the speed of 10m/s.
Ans.
According to the question:
Initial velocity (u) = 0, final velocity (v) = 10m/s, time (t) = 50 second, Mass (m) = 10000 kg,
Therefore, force (F)=?

⇒ 2000 kgms^-2 or, 2000 N
Thus required force = 2000 N

Q.4. An object gets 20 second to increase the speed from 10m/s to 50m/s. If the mass of the object is 1000 kg, what force will be required to do so?
Ans.
According to the question:
Initial velocity (u) = 10m/s, final velocity (v) = 50m/s, time (t) = 20 second, Mass (m) = 1000 kg,
Therefore, force (F) =?

F = ma = 1000 × 2 = 2000  N
Thus required force = 2000 N

Q.5. What force will be required to speed up a car having mass of 1200kg, from 5 m/s to 15m/s in 10 second?

Ans.
According to the question:-
Initial velocity (u) = 5m/s, final velocity (v) = 15m/s, time (t) = 10 second, Mass (m) = 1200 kg,
Therefore, force (F) =?

⇒ 1200 kg  × 1 ms^-2 ⇒ 1200 kgms^-2 or 1200 N
Thus required force = 1200 N

Q.6. In how much time an object having mass of 100kg will speed up from 5m/s to 25m/s, if 500N force will be applied over it?
Ans.
According to the question:
Initial velocity (u) = 5m/s, final velocity (v) = 25m/s, Mass (m) = 100 kg, Force (F) = 500N
Therefore, time (t) = ?

Thus required time = 4 second

Q.7. If a force of 1000 N is applied over a vehicle of 500 kg, then in how much time the speed of the vehicle will increase from 2 m/s to 10 m/s?
Ans.
According to the question:
Initial velocity (u) = 2m/s, final velocity (v) = 10m/s, Mass (m) = 500 kg, Force (F) = 1000N
Therefore, time (t) =?

Thus required time = 4 second

Q.8. A vehicle having mass equal to 1000 kg is running with a speed of 5m/s. After applying the force of 1000N for 10 second what will be the speed of vehicle?
Ans.
According to the question:
Mass of (m) = 1000 kg, Force, (F) = 1000 N, time (t) = 10s, Initial velocity (u) = 5m/s
Therefore, Final velocity (v) =?

⇒ 1000 kg m/s² × 10s = 1000 kg (v - 5m/s)
⇒ 10000 kg m/s = 1000 kg × v - 5000 kg m/s
⇒ 10000 kg m/s + 5000kg m/s = 1000kg × v
⇒ 15000 kgm/s = 1000 kg × v

Thus, the velocity of the vehicle will be 15m/s.

Q.9. An object gets the velocity of 10 m/s after applying a force of 500N for 5 second. If the mass of the object is equal to 1000 kg, what was its velocity before applying the force?
Ans.
According to the question:
Mass (m) = 1000 kg, Force (F) = 500N, time (t) = 10m/s, Final velocity (v) = 10m/s
Therefore, Initial velocity (u) =?


⇒ 500 kg ms^-2 × 10s = 10000 kg ms^-1-1000 kg × u
⇒ 5000 kg m/s = 10000 kg m/s - 1000 kg × u
⇒ 5000 kg m/s - 10000 kg m/s = -1000 kg × u
⇒ -5000kg m/s = -1000 kg × u

Thus speed of object was 5m/s

Type - V

Q.1. The acceleration of two objects are 5m/s² and 20m/s². If mass of both the object would be combined and a force of 50N would be applied on them, what will be their acceleration?
Ans.
In the order to calculate the acceleration of both the objects after combining their mass, first of all their mass will be calculated.
Ist object:
Given, Acceleration (a) = 20m/s²
Let the mass of one body = m₁
And a force of 50N will be applied over it.
We know that Force (F) = Mass (m) x Acceleration (a)
⇒ 50N = m₁ × 5ms^-2

2nd Object:
Given, Acceleration (a) = 20m/s²
Let the mass of one body = m₂
And a force of 50N will be applied over it.
We know that Force (F) = Mass (m) x Acceleration (a)
⇒ 50N = m₂ × 5 ms^-2

Now their total mass = m₁ + m₂ = 10 kg + 2.5 kg = 12.5 kg
In this condition:
Mass (m) = 12.5 kg, Force (F) = 50N, therefore, Acceleration (a) =?
We know that, F = m x a

Therefore, 50N = 12.5kg × a
Thus, Acceleration = 4 ms^-2