Recall and use the equation F = m a and know that the force and the acceleration are in the same direction

1.5.1 Effects of Forces

Learning Objective

Recall and use the equation \$F = ma\$ and understand that the force and the acceleration act in the same direction.

Key Concepts

• Force (\$F\$) – a push or pull acting on an object, measured in newtons (N).
• Mass (\$m\$) – the amount of matter in an object, measured in kilograms (kg).
• Acceleration (\$a\$) – the rate of change of velocity, measured in metres per second squared (m s⁻²).
• The relationship between them is given by Newton’s second law: \$\vec{F}=m\vec{a}\$
• The vector directions of \$\vec{F}\$ and \$\vec{a}\$ are the same; a force cannot produce acceleration in a different direction.

Derivation of the Equation

Starting from the definition of acceleration:

\$a = \frac{\Delta v}{\Delta t}\$

and the definition of momentum \$p = mv\$, Newton’s second law states that the net force equals the rate of change of momentum:

\$F = \frac{\Delta p}{\Delta t} = \frac{\Delta (mv)}{\Delta t} = m\frac{\Delta v}{\Delta t}=ma\$

Because mass is constant for most IGCSE problems, the equation simplifies to \$F = ma\$.

Direction of Force and Acceleration

Both \$\vec{F}\$ and \$\vec{a}\$ are vector quantities. The direction of the acceleration is exactly the same as the direction of the net external force acting on the object.

• If a force acts to the right, the acceleration is to the right.
• If multiple forces act, the net (resultant) force determines the direction of the acceleration.

Units and Symbols

Worked Example

Problem: A 2.0 kg cart is pulled horizontally by a constant force of 10 N. Find the acceleration of the cart and state its direction.

1. Write the formula: \$F = ma\$.
2. Rearrange for \$a\$: \$a = \dfrac{F}{m}\$.
3. Substitute the values: \$a = \dfrac{10\ \text{N}}{2.0\ \text{kg}} = 5\ \text{m s}^{-2}\$.
4. Since the force is horizontal to the right, the acceleration is also to the right.

Answer: \$a = 5\ \text{m s}^{-2}\$ to the right.

Common Misconceptions

• “A larger force always gives a larger acceleration, regardless of mass.” – The acceleration also depends on the mass; a larger mass reduces the acceleration for the same force.
• “Force and acceleration can be opposite in direction.” – By definition they are parallel; only the net force direction matters.
• “If an object moves, a force must be acting in the direction of motion.” – An object can continue moving due to inertia when no net force is present (Newton’s first law).

Practice Questions

1. A 5.0 kg block is pushed across a frictionless surface by a horizontal force of 20 N. Calculate the acceleration.
2. A 0.8 kg ball is dropped from rest. Ignoring air resistance, what is the net force acting on the ball just before it hits the ground? (Take \$g = 9.8\ \text{m s}^{-2}\$.)
3. Two forces act on a 3 kg object: 4 N to the east and 3 N to the north. Find the magnitude and direction of the resulting acceleration.