Physics 1 (Grade 10)
Measurement, motion in one and two dimensions, forces and Newton’s laws.
Measurement, motion in one and two dimensions, forces and Newton’s laws.
Units of the book
| Unit | What to know |
|---|---|
| Introduction | SI units and prefixes, significant figures, precision and accuracy |
| Representing motion | position and displacement, position–time graphs, velocity |
| Accelerated motion | acceleration, the motion equations, free fall |
| Forces in one dimension | Newton’s laws, weight, apparent weight, interaction forces |
| Forces in two dimensions | vectors and components, friction |
| Motion in two dimensions | projectiles, circular motion, relative velocity |
Formulas to remember
- v = v₀ + at: velocity
- d = v₀t + ½at²: displacement
- v² = v₀² + 2ad: without time
- F = ma: Newton’s second law
- W = mg: weight
- f = μN: friction
- a = v²/r: centripetal acceleration
- t = √(2h/g): fall time
🧠 Memory kit: motion and forces
| Formula | In plain words | How to remember it |
|---|---|---|
| v̄ = Δd / Δt, a = Δv / Δt | Velocity = change in position per second; acceleration = change in velocity per second. | Both are “change ÷ time”; acceleration is “the speed of the speed”. |
| v = v₀ + at | Final velocity after time t (no distance needed). | Start at v₀ and add a every second. |
| d = v₀t + ½at² | Distance after time t (no final velocity needed). | It is the area under the v–t graph: a rectangle v₀t plus a triangle ½at². |
| v² = v₀² + 2ad | The one with no time. | If time is neither given nor asked for, this is your equation. |
| d = ½(v₀ + v)t | Distance = average velocity × time (no acceleration). | Average of start and end, because the velocity changes steadily. |
| g = 9.8 m/s² (≈ 10) | Free-fall acceleration, downwards. | A falling object gains about 10 m/s every second. |
| t = √(2h/g), h = v₀² / 2g | Time to fall from height h, and the top height of an object thrown up at v₀. | From d = ½at² and v² = v₀² + 2ad with v = 0 at the top. |
| ΣF = ma | Newton’s second law: net force = mass × acceleration. | Push harder → more acceleration; more mass → less. |
| W = mg | Weight is a force (newtons); mass is the amount of matter (kg). | On the Moon your mass is the same; your weight is not. |
| N = m(g + a) | N = m(g − a) | Apparent weight in a lift accelerating up (more) or down (less); zero in free fall. | You feel heavy when the lift starts going up. |
| f = μN | Friction = coefficient × normal force. Maximum static friction is bigger than kinetic. | Starting a box moving is harder than keeping it moving. |
| F∥ = mg sinθ, N = mg cosθ | On a slope: the parallel part pulls the object down; the perpendicular part presses it on the surface. | At θ = 0 (flat ground) no pull (sin 0 = 0) and full press (cos 0 = 1). |
| Aₓ = A cosθ, A y = A sinθ | Components of a vector at angle θ to the horizontal. | cos sits next to the angle (across); sin is opposite it (up). |
| R = √(Aₓ² + A y ²), tanθ = A y / Aₓ | Adding vectors by components. | Add the across parts and the up parts separately, then use Pythagoras. |
| a c = v² / r, F c = mv² / r | Centripetal acceleration and force, towards the centre. | Double the speed → four times the force. |
| R = v₀² sin2θ / g | Range of a projectile on level ground; greatest at 45°. | Across: constant speed; up and down: free fall. “Two separate motions.” |
🧠 Memory kit: graphs, the three laws and prefixes
| Topic | What to know |
|---|---|
| Position–time graph | slope = velocity. Flat → at rest, straight sloped line → constant velocity, curve → accelerating. |
| Velocity–time graph | slope = acceleration, area under it = displacement. |
| Acceleration–time graph | area under it = change in velocity. |
| Newton’s first law | inertia: an object stays at rest or at constant velocity unless a net force acts. Mass measures inertia. |
| Newton’s third law | every action has an equal and opposite reaction, acting on two different bodies, so they never cancel. |
| Big prefixes | giga G = 10⁹, mega M = 10⁶, kilo k = 10³ |
| Small prefixes | centi c = 10⁻², milli m = 10⁻³, micro μ = 10⁻⁶, nano n = 10⁻⁹, pico p = 10⁻¹² |
| Precision and accuracy | precision: how close readings are to each other. Accuracy: how close they are to the true value. |
| Significant figures | all non-zero digits count, zeros between them count, leading zeros do not (0.0045 has two), trailing zeros after a decimal point count. |
- Picking a motion equation: each one leaves out one quantity. List what you have and what you want; the missing quantity tells you which equation to use.
- Units guard the formula: newton = kg·m/s², hence F = ma. If you forget a formula, make the units on both sides match.
- “Starts from rest” means v₀ = 0, “comes to a stop” means v = 0, and “highest point” means vertical velocity = 0.
A way of memorizing that sticks
- Understand before you memorize: read “in plain words” for each formula and say out loud what it measures and why each quantity is multiplied or divided. A formula you understand takes a minute to learn.
- Active recall: cover the formula column and write it from memory, then check. Writing from memory beats rereading by far.
- Spaced repetition: review the same sheet after 1 day, 3 days, a week and two weeks. Four short reviews lock it in until test day.
- Your own formula page: write every formula of a book on one page by hand. If it does not fit, you are writing things you can derive, so cut them.
- Teach it: explain the formula to a friend, or to yourself in a mirror, in two sentences. If you cannot explain it, you do not know it yet.
- Use it at once: after each group, press “Try one” in the patterns below. Memory sets when you use it.
Question patterns
Prefixes and conversion
kilo 10³, mega 10⁶, giga 10⁹, centi 10⁻², milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹.
Significant figures
Leading zeros never count; trailing zeros after a decimal point do.
Motion equations and free fall
List v₀, v, a, t, d and choose the equation with only your unknown.
Motion graphs
Slope of x–t = velocity; slope of v–t = acceleration; area under v–t = displacement.
Newton’s laws and friction
A lift accelerating up increases apparent weight: m(g + a).
Vectors
Perpendicular forces: resultant by Pythagoras. Horizontal component F cos θ.
Motion in two dimensions, relative velocity
Horizontal velocity is constant; vertical motion is free fall; vertical velocity is zero at the top.
- Mass (kg) is not weight (N).
- Centripetal acceleration points inwards, not outwards.
More patterns (figures and calculations)
Position–time graphs
Slope = velocity; a flat line = at rest.
Velocity–time graphs
Slope = acceleration; area = displacement.
Inclined planes
a = (F − mg sin θ)/m
Velocity components
vₓ = v cos θ, v y = v sin θ