Mechanics (Edexcel IAL Physics Unit 1 WPH11)

Q: What value of g should I use for calculations?

Always use as specified on the exam data sheet, unless the question explicitly tells you to use a different value.

Edexcel International A-Level Physics· 2018 Specification Issue 3, Section 1.3, Statements 1-22· 45 min read

🎯 Learning objectives

1.
Use suvat equations to solve 1D uniformly accelerated motion problems
2.
Interpret and draw displacement/velocity/acceleration graphs for uniform and non-uniform motion
3.
Resolve vectors into perpendicular components and calculate coplanar resultant vectors
4.
Solve projectile motion problems using independent horizontal and vertical motion
5.
Draw free-body diagrams and apply Newton's laws of motion to force problems
6.
Apply conservation of linear momentum to 1D collision and explosion scenarios
7.
Use the principle of moments and centre of gravity to solve equilibrium problems
8.
Calculate work, kinetic energy, gravitational potential energy, power and efficiency using conservation of energy
9.
Describe Core Practical 1 for measuring the acceleration of a freely falling object

1. 1. Kinematics: Uniform Motion and Motion Graphs★★☆☆☆⏱ 10 min

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📘 Definition

Uniformly Accelerated Motion

Motion where acceleration is constant over time, allowing use of the four suvat equations to calculate unknown quantities.

For 1D uniformly accelerated motion, use the suvat equations, where $s$ = displacement, $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $t$ = time taken. All equations are provided on your exam data sheet, so select the equation that excludes the unknown quantity you do not need to calculate.

📐 Worked Example

A car accelerates uniformly from rest to 18 m s⁻¹ over a displacement of 100 m. Calculate the acceleration of the car.

1
List known values: $u = 0 m s^{- 1}$ , $v = 18 m s^{- 1}$ , $s = 100 m$ , $a = ?$
2
Select suvat equation with no $t$ term: $v^{2} = u^{2} + 2 a s$
3
Rearrange for $a$ : $a = \frac{v ^{2} - u ^{2}}{2 s}$
4
Substitute values: $a = \frac{1 8 ^{2} - 0}{2 \times 100} = 1.62 m s^{- 2}$ (3 sf)

For motion graphs:

Displacement-time ( $s$ - $t$ ) graph gradient = velocity; use tangent gradient for instantaneous velocity, average gradient for average velocity
Velocity-time ( $v$ - $t$ ) graph gradient = acceleration; area under graph = total displacement
Acceleration-time ( $a$ - $t$ ) graph area under graph = change in velocity

For non-uniform acceleration, estimate area using the trapezium rule or counting squares, and calculate gradients using tangents to the curve.

Exam tip:

Always label graph axes with units when drawing motion graphs, and clearly draw tangent lines on curves when calculating instantaneous gradients to gain full marks.

2. 2. Vectors and Projectile Motion★★★☆☆⏱ 8 min

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📘 Definition

Vector Resolution

The process of splitting a single vector into two perpendicular components, which can be treated independently in calculations.

Resolve any vector $V$ at angle $θ$ to the horizontal into components: horizontal $V_{x} = V cos θ$ , vertical $V_{y} = V sin θ$ . For two perpendicular vectors, find the resultant magnitude using Pythagoras' theorem and direction using arctangent. For non-perpendicular coplanar vectors, use scale drawing to find the resultant.

📐 Worked Example

A ball is kicked with an initial velocity of 15 m s⁻¹ at an angle of 30° above the horizontal. Calculate the horizontal and vertical components of the initial velocity.

1
Known values: $V = 15 m s^{- 1}$ , $θ = 3 0^{\circ}$
2
Horizontal component: $V_{x} = 15 cos 3 0^{\circ} = 13.0 m s^{- 1}$ (3 sf)
3
Vertical component: $V_{y} = 15 sin 3 0^{\circ} = 7.5 m s^{- 1}$

Projectile motion treats horizontal and vertical motion as fully independent: horizontal velocity is constant (no air resistance, no horizontal force), while vertical motion is uniformly accelerated by gravity at $9.81 m s^{- 2}$ downwards. Calculate time of flight using vertical motion first, then use constant horizontal velocity to find horizontal distance travelled.

Exam tip:

Always assign a positive direction (e.g. upwards = positive) for vertical motion, so gravitational acceleration is written as $- 9.81 m s^{- 2}$ for upward motion calculations.

3. 3. Forces and Newton's Laws of Motion★★★☆☆⏱ 9 min

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📘 Definition

Free-Body Diagram

A simplified diagram showing all forces acting on a single isolated object, with force arrows drawn to scale in the correct direction and clearly labelled.

Key laws of motion:

Newton's First Law: An object remains at rest or moves at constant velocity if resultant force on it is zero
Newton's Second Law: $\sum F = ma$ (resultant force = mass × acceleration)
Newton's Third Law: Interacting objects exert equal, opposite, same-type forces on each other, acting on different objects

Weight of an object is

W = m g

, where

g = 9.81 m s^{- 2}

. Terminal velocity occurs when drag force equals the weight of a falling object, so resultant force is zero and speed is constant.

📐 Worked Example

A 2.5 kg box is pushed across a flat floor with a horizontal force of 12 N, facing a constant frictional force of 4.5 N. Calculate the acceleration of the box.

1
Calculate resultant horizontal force: $\sum F = 12 - 4.5 = 7.5 N$
2
Rearrange $\sum F = ma$ for acceleration: $a = \frac{\sum F}{m}$
3
Substitute values: $a = \frac{7.5}{2.5} = 3.0 m s^{- 2}$

Exam tip:

Always identify all forces acting on the object (weight, normal reaction, friction, drag, applied force, tension) before calculating resultant force to avoid missing terms.

4. 4. 1D Linear Momentum and Conservation★★★☆☆⏱ 7 min

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📘 Definition

Linear Momentum

Momentum $p = m v$ , where $m$ = mass, $v$ = velocity, units $kg m s^{- 1}$ . It is a vector quantity, so direction must be included in calculations.

Conservation of linear momentum states that the total momentum of a closed system remains constant if no external resultant force acts on it. This applies to all 1D collisions and explosions, and is derived directly from Newton's Second and Third Laws of motion.

📐 Worked Example

A 2 kg trolley moving at 3 m s⁻¹ right collides with a stationary 1 kg trolley. After collision, the 2 kg trolley moves at 1 m s⁻¹ right. Calculate the velocity of the 1 kg trolley after collision.

1
Total momentum before collision: $(2 \times 3) + (1 \times 0) = 6 kg m s^{- 1}$ (right = positive)
2
Total momentum after collision: $(2 \times 1) + (1 \times v) = 2 + v$
3
Equate total momentum before and after: $6 = 2 + v$ → $v = 4 m s^{- 1}$ (right direction)

Exam tip:

Always assign a positive direction at the start of 1D momentum calculations, and use negative values for velocities in the opposite direction to avoid sign errors.

5. 5. Moments and Equilibrium★★★☆☆⏱ 7 min

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📘 Definition

Moment of a Force

Moment = force × perpendicular distance from the pivot to the line of action of the force, units $N m$ . Moments can be clockwise or anticlockwise.

Centre of gravity is the point where the entire weight of an object can be considered to act. For an object in equilibrium:

Sum of clockwise moments about any pivot = sum of anticlockwise moments about the same pivot
Resultant force on the object is zero

For uniform objects, weight acts at the midpoint of the object.

📐 Worked Example

A uniform 1 m long see-saw of weight 50 N is pivoted at its centre. A 300 N child sits 0.3 m left of the pivot. How far right of the pivot must a 200 N child sit to balance the see-saw?

1
Anticlockwise moment from 300 N child: $300 \times 0.3 = 90 N m$
2
Clockwise moment from 200 N child: $200 \times d$
3
Equate moments for equilibrium: $200 d = 90$ → $d = 0.45 m$ right of pivot

Exam tip:

Always include the moment from the weight of a uniform object if the pivot is not at its midpoint, as this is a common missed term in equilibrium questions.

6. 6. Work, Energy, Power and Efficiency★★★☆☆⏱ 8 min

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📘 Definition

Work Done

Work done $Δ W = F Δ s cos θ$ , where $θ$ is the angle between force $F$ and displacement $Δ s$ , units Joules (J). If force is aligned with displacement, $cos θ = 1$ so $Δ W = F Δ s$ .

Key energy formulae:

Kinetic energy: $E_{k} = \frac{1}{2} m v^{2}$
Gravitational potential energy change: $Δ E_{g r a v} = m g Δ h$

Conservation of energy states energy cannot be created or destroyed, only converted between forms. Power

P = \frac{work done}{time taken} = \frac{energy transferred}{time taken}

, units Watts (W). Efficiency =

\frac{useful energy output}{total energy input} = \frac{useful power output}{total power input}

, often expressed as a percentage.

📐 Worked Example

A 50 kg student climbs 2.5 m up stairs in 3.2 s. Calculate the useful power output of the student.

1
Calculate gravitational potential energy gained: $Δ E_{g r a v} = 50 \times 9.81 \times 2.5 = 1226.25 J$
2
Calculate power: $P = \frac{E}{t} = \frac{1226.25}{3.2} = 383 W$ (3 sf)

Exam tip:

Efficiency is always less than 1 (or 100%) because some energy is always lost as heat, sound or other waste forms, so answers above 100% are always incorrect.

7. Common Pitfalls

Wrong move:

Forgetting to assign direction for vectors (velocity, force, momentum) in calculations

Why:

Vectors have direction, so opposite directions require negative values to get correct results

Correct move:

Define a positive direction at the start of all vector calculations, use negative values for opposite directions

Wrong move:

Using calculus (differentiation/integration) for non-uniform acceleration problems

Why:

Calculus is not permitted in Unit 1, you will lose marks even if your final answer is correct

Correct move:

Use tangent gradients for instantaneous rates and area under graphs for displacement/change in velocity

Wrong move:

Treating horizontal velocity of a projectile as accelerating

Why:

There is no horizontal force acting on a projectile (ignoring air resistance), so horizontal velocity is constant

Correct move:

Use constant velocity $s = v t$ for horizontal projectile motion, use suvat equations only for vertical motion

Wrong move:

Omitting the weight of a uniform object in moment calculations when the pivot is not at its centre

Why:

The weight of the object acts at its centre of mass, so it exerts a moment around the pivot if not aligned

Correct move:

Always include the moment from the object's weight if the pivot is not at its midpoint

Wrong move:

Using $g = 10 m s^{- 2}$ instead of $9.81 m s^{- 2}$

Why:

The exam data sheet specifies $g = 9.81 m s^{- 2}$ , so using 10 leads to rounding errors and lost marks

Correct move:

Always use $g = 9.81 m s^{- 2}$ unless explicitly told otherwise in the question

8. Quick Reference Cheatsheet

Concept	Key Formula/Rule	Exam Reminder
SUVAT Equations	$s = (u + v) t /2$ , $v = u + a t$ , $s = u t + ½ a t^{2}$ , $v^{2} = u^{2} + 2 a s$	Choose equation that excludes the unneeded unknown value
Motion Graphs	$s$ - $t$ gradient = velocity, $v$ - $t$ gradient = acceleration, $v$ - $t$ area = displacement	Use tangents for non-uniform motion gradients
Vectors	$V_{x} = V cos θ$ , $V_{y} = V sin θ$ , resultant = $V_{x}^{2} + V_{y}^{2}$	Assign positive direction for all vector calculations
Projectiles	Horizontal v constant, vertical $a = 9.81 m s^{- 2}$ downwards	Calculate time of flight using vertical motion first
Newton's Laws	$\sum F = ma$ , $W = m g$	Draw free-body diagrams to identify all forces first
1D Momentum	$p = m v$ , total $p$ before = total $p$ after	Use negative signs for opposite direction velocities
Moments	Moment = $F \times$ perpendicular distance, sum clockwise = sum anticlockwise	Include uniform object weight at its midpoint
Work/Energy/Power	$Δ W = F Δ s cos θ$ , $E_{k} = ½ m v^{2}$ , $P = E / t$ , efficiency = useful/total	Efficiency is always less than 100%

9. Frequently Asked

Do I need to memorise suvat equations for the WPH11 exam?

No, all required mechanics equations are provided on the official exam data sheet. You only need to know how to rearrange and apply them correctly for different scenarios.

Can I use calculus to solve non-uniform acceleration problems?

No, calculus is not accepted for Unit 1 answers. You must use tangent gradients for instantaneous rates and area under graphs to calculate displacement or change in velocity for non-uniform motion.

What value of g should I use for calculations?

Always use $g = 9.81 m s^{- 2}$ as specified on the exam data sheet, unless the question explicitly tells you to use a different value.

Going deeper

Official SpecificationEdexcel IAL Physics 2018 SpecificationOfficial reference for Unit 1 Mechanics content

What's Next

Now you have mastered the core Mechanics content for Edexcel IAL Physics Unit 1 WPH11, you can move on to the second part of Unit 1: Materials, which covers Hooke's law, stress, strain, density and viscosity. You should also practice past paper questions specifically for Mechanics to reinforce your understanding, paying close attention to command terms and mark scheme requirements. Make sure you can carry out calculations for Core Practical 1 and explain sources of error for free fall experiments, as these are commonly tested in both multiple choice and structured questions.