A football of mass 0.45 kg is at rest on the ground. A player's boot applies a force of 90 N to it. (i) Using

Concept understanding — Newton's Second Law

Newton's Second Law: The Law That Connects Force, Mass, and Motion

Imagine pushing a shopping cart. If you give it a gentle shove, it rolls slowly and stops quickly. If you shove it hard, it speeds away and keeps going much farther. Now imagine pushing an empty cart versus one loaded with groceries. Even with the same shove, the full cart moves much less. You already know this instinctively — but Newton's Second Law is the precise idea behind that intuition.

The Core Idea

Newton's Second Law states that the force applied to an object determines how much its motion changes — and that change depends on the object's mass. In plain language: the harder you push, the more the object speeds up; the heavier the object, the harder it is to speed up.

This is not about motion itself, but about change in motion. A car cruising at a steady speed on a highway has no net force acting on it — the engine's push is exactly balanced by air resistance and road friction. Force is what breaks that steady state: it accelerates, decelerates, or changes direction.

Important

Newton's Second Law is the bridge between cause (force) and effect (change in motion). Without it, we could describe motion but never explain why it starts, stops, or turns.

What "Change in Motion" Really Means

The law says that force produces a change in motion — and that change happens in the same direction as the force. If you push a box east, it moves east. If you push it north, it moves north. The change is not random; it follows the push.

But the amount of change also depends on mass. Mass is not weight — it is the measure of how much matter an object contains, and more fundamentally, how much it resists being moved. A feather and a brick both have mass, but the brick has far more. The same force that sends the feather flying will barely budge the brick.

A small force on a light object produces a large change in motion.
The same small force on a heavy object produces only a tiny change.
A large force on a heavy object can produce the same change as a small force on a light one.

This is why a truck needs a much bigger engine than a bicycle — the truck's huge mass requires a much larger force to achieve the same acceleration.

Why It Matters Beyond Physics

This law is not just for engineers. It shapes how we understand the world every day.

When you brake a car, the brake pads apply a force opposite to the car's motion. The heavier the car (or the faster it is going), the more force the brakes must apply to stop it in the same distance. That is why loaded trucks take longer to stop — and why safe following distances exist. …

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This problem applies Newton's Second Law of Motion to calculate the acceleration of a football when kicked and its final speed, demonstrating how force and contact time influence the ball's velocity.

Understanding how forces affect motion is fundamental in Physical Education, especially in sports like football. The key concept here is Newton's Second Law of Motion, which describes the relationship between an object's mass, the force applied to it, and the resulting acceleration.

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that if you apply a larger force to an object, it will accelerate more rapidly, and if an object has more mass, it will accelerate less for the same amount of force. In the context of kicking a football, the player's boot applies a force to the ball, causing it to accelerate from rest to a certain speed. The magnitude of this acceleration, and consequently the final speed of the ball, depends on how hard the player kicks (the force applied) and the mass of the ball.

(i) Using F = ma, calculate the acceleration of the ball.

To calculate the acceleration, we use Newton's Second Law of Motion.

The given values are:

Mass of the football (m) = 0.45 kg
Force applied by the boot (F) = 90 N

F = ma

Where:

F is the net force acting on the object (in Newtons, N)
m is the mass of the object (in kilograms, kg)
a is the acceleration of the object (in meters per second squared, m/s²)

We need to find a, so we rearrange the formula to a = F/m.

Substitute the given values into the formula: a = (90 N)/(0.45 kg)
Perform the calculation: a = 200 m/s²

The acceleration of the ball is 200 m/s².

(ii) If the boot stays in contact with the ball for 0.02 s, calculate the speed with which the ball leaves the foot.

To calculate the final speed, we use a kinematic equation that relates initial velocity, acceleration, time, and final velocity.

The known values are:

Initial velocity (u) = 0 m/s (since the ball is at rest)
Acceleration (a) = 200 m/s² (calculated in part i)
Time of contact (t) = 0.02 s

v = u + at

Where:

v is the final velocity (in meters per second, m/s)
u is the initial velocity (in meters per second, m/s)
a is the acceleration (in meters per second squared, m/s²)
t is the time (in seconds, s)

Substitute the known values into the formula: v = 0 m/s + (200 m/s²)(0.02 s)
Perform the calculation: v = 0 + 4 m/s v = 4 m/s

The speed with which the ball leaves the foot is 4 m/s.

(iii) State which of Newton's laws you have used and what the result tells the coach about kicking harder.

The law used in part (i) to calculate the acceleration of the ball is Newton's Second Law of Motion.

The results from these calculations tell a coach important information about how to kick harder, meaning how to achieve a higher final speed for the ball: …

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Q.A football of mass 0.45 kg is at rest on the ground. A player's boot applies a force of 90 N to it.

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