Forces & Motion (Basics)
Learn how engineers describe pushes, pulls, weight and movement. Calculate resultant forces, weight from mass, speed and acceleration — the foundations of mechanical engineering science.
2Topics
8Examples
4Calculators
12Practice Qs
💪Forces & WeightNewtons, W = mg, resultants
🚗MotionSpeed & acceleration
⚙️Applications4 workshop calculators
🎮Game12 randomised questions
📝Practice12 graded questions
Why this matters in engineeringReal world
Every crane lift, conveyor line, and vehicle brake test relies on these four ideas. Weight tells you what a hoist must hold. Resultant force tells you whether a machine part will stay still or start to move. Speed and acceleration tell you how quickly a product moves down a line or how safely a vehicle can stop.
💪
Forces & Weight
Measuring pushes and pulls in newtons, finding weight from mass, and combining forces in a straight line.
🧮Force ToolkitChoose a mode, enter values, press Calculate
Enter your values above and press Calculate to see every working step.
📚 Key vocabulary
- Force
- a push or a pull, measured in newtons (N).
- Mass
- the amount of matter in an object, measured in kilograms (kg). It does not change with location.
- Weight
- the force of gravity pulling on a mass, measured in newtons (N).
- Gravitational field strength (g)
- 9.81 N/kg on Earth — the pull on each kilogram.
- Resultant force
- the single force that has the same effect as all the forces acting together.
- Balanced forces
- resultant is zero — the object stays still or keeps a steady speed.
👁️ Visual aid — two opposite forces on a machine block and their resultant
✍️Worked example 1 — weight of a motor
QuestionAn electric motor has a mass of 25 kg. Calculate its weight. Take g = 9.81 N/kg.
Formula
W = m × gSubstitute
W = 25 × 9.81Multiply
25 × 9.81 = 245.25AnswerW = 245.25 N ≈ 245 N (3 significant figures)
✍️Worked example 2 — two forces, same direction
QuestionTwo technicians push a trolley in the same direction with forces of 60 N and 40 N. Find the resultant force.
RuleSame direction → add the forces.
Substitute
R = 60 + 40Add
60 + 40 = 100AnswerResultant = 100 N in the direction of the pushes.
✍️Worked example 3 — opposite forces (engineering context)
QuestionA pallet is pushed forward with a force of 250 N while friction pulls back with 180 N. Find the resultant force and its direction.
RuleOpposite directions → subtract the smaller force from the larger force.
Substitute
R = 250 − 180Subtract
250 − 180 = 70AnswerResultant = 70 N forward (the direction of the larger, 250 N force). The pallet accelerates forward.
✍️Worked example 4 — force to accelerate a trolley
QuestionA workshop trolley of mass 80 kg must be accelerated at 1.5 m/s². What resultant force is needed?
Formula
F = m × aSubstitute
F = 80 × 1.5Multiply
80 × 1.5 = 120AnswerF = 120 N
🚗
Motion — Speed & Acceleration
Describing how far, how fast and how quickly speed changes — the language of conveyor lines, vehicles and machines.
⏱️Motion CalculatorChoose a mode, enter values, press Calculate
Enter your values above and press Calculate to see every working step.
📚 Key vocabulary
- Speed
- how fast something moves — distance covered each second (m/s).
- Velocity
- speed in a stated direction.
- Acceleration
- how quickly speed changes each second (m/s²).
- Deceleration
- a negative acceleration — the object slows down.
- Average speed
- total distance divided by total time for the whole journey.
- Distance–time graph
- a straight sloped line means steady speed; a flat line means stopped.
👁️ Visual aid — a parcel on a conveyor: steady speed on a distance–time graph
✍️Worked example 5 — conveyor speed
QuestionA parcel travels 18 m along a conveyor in 12 s. Calculate the speed of the belt.
Formula
speed = distance ÷ timeSubstitute
speed = 18 ÷ 12Divide
18 ÷ 12 = 1.5Answerspeed = 1.5 m/s
✍️Worked example 6 — rearranging for time
QuestionAn automated guided vehicle moves at 2.5 m/s. How long does it take to travel 60 m?
Formula
speed = distance ÷ time rearranged to time = distance ÷ speedSubstitute
time = 60 ÷ 2.5Divide
60 ÷ 2.5 = 24Answertime = 24 s
✍️Worked example 7 — acceleration of a test vehicle
QuestionA test vehicle accelerates from rest (u = 0 m/s) to v = 24 m/s in 8 s. Calculate the acceleration.
Formula
a = (v − u) ÷ tSubstitute
a = (24 − 0) ÷ 8Subtract
24 − 0 = 24Divide
24 ÷ 8 = 3Answera = 3 m/s²
✍️Worked example 8 — braking deceleration
QuestionA delivery van slows from 30 m/s to a stop (v = 0 m/s) in 6 s. Calculate the acceleration and state what the sign means.
Formula
a = (v − u) ÷ tSubstitute
a = (0 − 30) ÷ 6Subtract
0 − 30 = −30Divide
−30 ÷ 6 = −5Answera = −5 m/s² — the negative sign shows a deceleration of 5 m/s².
⚙️
Engineering Applications
Four workshop calculators that use forces and motion every working day.
🏗️ Crane hoist — load weight check
Before a lift, the crane operator must know the load's weight in newtons so the hoist rating is not exceeded.
W = m × g (g = 9.81 N/kg)
🧮 Calculator
Enter the load mass and press Calculate.
🔨 Bracket test — resultant of two in-line forces
A mounting bracket is loaded from both ends during testing. The resultant decides whether the fixings hold.
Same direction: add | Opposite: subtract, keep larger direction
🧮 Calculator
Enter both forces and press Calculate.
📦 Conveyor line — belt speed
Production planners set the takt time from the belt speed: distance between stations divided by travel time.
speed = distance ÷ time
🧮 Calculator
Enter distance and time, then press Calculate.
🚗 Brake test — deceleration
Vehicle technicians check that brakes produce a large enough deceleration to pass the safety test.
a = (v − u) ÷ t
🧮 Calculator
Enter the speeds and time, then press Calculate.
🎮
Forces & Motion Challenge
12 randomised questions per round. New numbers every time you play.
⚡ Quick-fire round
Question 1 / 12
Score: 0
Streak: 0 🔥
Press Start to begin!
📝
Practice Questions
12 graded questions. Attempt each one on paper first, then reveal the full worked solution.
Take g = 9.81 N/kg throughout. Show every step of your working, including the formula and the substitution.
Question 1 · Forces2 marks
Calculate the weight of a 10 kg toolbox.
W = m × g
W = 10 × 9.81
W = 98.1 N (1 mark substitution, 1 mark answer)
W = 10 × 9.81
W = 98.1 N (1 mark substitution, 1 mark answer)
Question 2 · Forces1 mark
Two forces of 35 N and 45 N act on a component in the same direction. State the resultant force.
Same direction → add: 35 + 45 = 80 N
Question 3 · Forces2 marks
A winch pulls a skip forward with 300 N while friction resists with 120 N. Find the resultant force and its direction.
Opposite directions → subtract: 300 − 120 = 180
Resultant = 180 N forward (direction of the larger force)
Resultant = 180 N forward (direction of the larger force)
Question 4 · Forces2 marks
What resultant force accelerates a 50 kg trolley at 2 m/s²?
F = m × a
F = 50 × 2
F = 100 N
F = 50 × 2
F = 100 N
Question 5 · Forces2 marks
A component has a weight of 490.5 N. Calculate its mass.
W = m × g rearranged m = W ÷ g
m = 490.5 ÷ 9.81
m = 50 kg
m = 490.5 ÷ 9.81
m = 50 kg
Question 6 · Motion1 mark
A robot travels 240 m in 60 s. Calculate its speed.
speed = distance ÷ time = 240 ÷ 60 = 4 m/s
Question 7 · Motion2 marks
A belt moves at 3 m/s for 45 s. How far does a product travel?
distance = speed × time
distance = 3 × 45
distance = 135 m
distance = 3 × 45
distance = 135 m
Question 8 · Motion2 marks
How long does a forklift travelling at 12.5 m/s take to cover 500 m?
time = distance ÷ speed
time = 500 ÷ 12.5
time = 40 s
time = 500 ÷ 12.5
time = 40 s
Question 9 · Motion2 marks
A machine carriage speeds up from 4 m/s to 16 m/s in 6 s. Calculate its acceleration.
a = (v − u) ÷ t
a = (16 − 4) ÷ 6 = 12 ÷ 6
a = 2 m/s²
a = (16 − 4) ÷ 6 = 12 ÷ 6
a = 2 m/s²
Question 10 · Motion3 marks
A vehicle starts at u = 5 m/s and accelerates at 1.2 m/s² for 10 s. Use v = u + (a × t) to find its final speed.
v = u + (a × t)
v = 5 + (1.2 × 10)
v = 5 + 12
v = 17 m/s
v = 5 + (1.2 × 10)
v = 5 + 12
v = 17 m/s
Question 11 · Motion2 marks
A lorry slows from 20 m/s to 8 m/s in 4 s. Calculate the acceleration and state the deceleration.
a = (v − u) ÷ t = (8 − 20) ÷ 4 = −12 ÷ 4 = −3 m/s²
Deceleration = 3 m/s²
Deceleration = 3 m/s²
Question 12 · Combined3 marks
A forklift lifts a 1200 kg pallet. Calculate the weight of the pallet in newtons, then give your answer in kilonewtons to 2 decimal places.
W = m × g = 1200 × 9.81 = 11772 N
Convert: 11772 ÷ 1000 = 11.77 kN
Convert: 11772 ÷ 1000 = 11.77 kN