Motion and Forces

Step 1 — State the formula:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} = \frac{\Delta s}{\Delta t} $$

Step 2 — Substitute the values:

$$ v = \frac{150}{30} $$

Answer: $v = 5\,\text{m/s}$

Rearranged formula: $$ \text{distance} = \text{speed} \times \text{time}, \qquad s = vt $$

Substitute: $$ s = 12 \times 15 $$

Answer: $s = 180\,\text{m}$

Rearranged formula: $$ t = \frac{s}{v} = \frac{200}{80} $$

Answer: $t = 2.5\,\text{h}$, which is $2.5 \times 60 = 150\,\text{minutes}$.

Calculation: $$ v = \frac{3\,\text{km}}{100/3600\,\text{h}} = 3 \times 36 = 108\,\text{km/h} $$ This is above the $100\,\text{km/h}$ limit, so the car appears to have broken the speed limit.

Benefit: Because average speed is measured continuously over the whole stretch, a driver cannot simply brake sharply at a single camera location and then speed up again immediately afterwards (as can happen with single-point cameras). This encourages drivers to keep to a consistently safer speed along the entire road, including at points between the two cameras where hazards such as junctions or pedestrians may be present.

Drawback: Because only the average is measured, this system cannot detect a dangerous momentary top speed that still results in a compliant average — for example, a brief unsafe overtaking manoeuvre followed by driving well under the limit for the rest of the stretch. An average speed within the limit does not guarantee the driver's speed was safe and steady the whole way.

Benefit: Automatically reducing speed in crowded areas lowers both the risk and the severity of collisions with pedestrians, since a scooter moving much more slowly gives both the rider and pedestrians more time to react, and a shorter distance is needed to stop — without relying on riders remembering or choosing to slow down themselves.

Drawback: GPS position readings can be inaccurate by several metres, especially between tall buildings, so the speed limiter might engage a little too early or too late at a genuine boundary. Riders may feel unfairly restricted if it engages incorrectly, or pedestrians could be put at risk if it fails to engage in time; continuously tracking the location of individual scooters also raises questions about how that movement data is stored and who can access it.

Calculation: Time at $100\,\text{km/h}$: $\dfrac{200}{100}=2\,\text{h}=120\,\text{min}$. Time at $120\,\text{km/h}$: $\dfrac{200}{120}=1.667\,\text{h}\approx100\,\text{min}$. Time saved $\approx 20\,\text{minutes}$ per $200\,\text{km}$ trip.

Benefit: A $20$-minute saving on one long trip seems modest, but across many drivers making similar journeys every day, the accumulated time saved is significant — supporting business productivity, reducing driver fatigue on very long trips, and potentially helping emergency vehicles reach incidents faster.

Drawback: The historical data shows higher motorway speed limits are associated with more serious accidents — consistent with higher speeds increasing both stopping distances and the force involved in any collision that does occur, making crashes at $120\,\text{km/h}$ more likely to be fatal than at $100\,\text{km/h}$. Higher speeds also increase air resistance sharply, increasing fuel consumption and CO₂ emissions per trip even as journey time falls.

Evaluation: A relatively modest average time saving of around $20$ minutes on a long trip needs to be weighed carefully against a real, well-documented increase in accident risk and severity — a reasonable case for caution rather than a clear-cut decision either way.

Step 1 — State the formula:

$$ \text{speed} = \frac{\text{distance}}{\text{time}} = \frac{\Delta s}{\Delta t} $$

Step 2 — Substitute the values:

$$ v = \frac{150}{10} $$

Step 3 — Calculate:

$$ v = 15 $$

Answer: $v = 15\,\text{m/s}$

Step 1 — Find the change in distance and change in time:

$$ \Delta s = 30 - 10 = 20\,\text{m} \qquad \Delta t = 6 - 2 = 4\,\text{s} $$

Step 2 — Apply the speed formula:

$$ v = \frac{\Delta s}{\Delta t} = \frac{20}{4} $$

Answer: $v = 5\,\text{m/s}$

The distance a car covers in its "thinking time" (before braking even begins) is speed $\times$ time — a faster car covers a much greater distance in the same reaction time than a slower one. At $30\,\text{m/s}$, in a $2\,\text{s}$ reaction time the car has already travelled $30\times2=60\,\text{m}$ before braking starts, before any braking distance is added. Near a school, where children may step into the road with little warning, a lower speed limit directly reduces both this "thinking distance" and the total stopping distance, giving the driver more time and a shorter distance to stop safely. This is exactly the relationship shown by the gradient of a distance–time graph: a steeper gradient (higher speed) means more distance is covered for every second that passes — which is why speed limits are set lower where sudden hazards are more likely.

Benefit: Average speed dropped substantially, from $48\,\text{km/h}$ to $22\,\text{km/h}$, more than halving it. A lower speed reduces both the distance a vehicle travels during a driver's reaction time and its stopping distance once braking, likely reducing the number and severity of accidents on a residential road, especially where pedestrians are present.

Drawback: The time to travel $1\,\text{km}$ more than doubled, from $1.25$ to $2.7$ minutes. Over many journeys, and for emergency vehicles like ambulances that may need to use the road, this extra time could be significant — delaying urgent responses, as well as increasing journey times, fuel use, and vehicle wear for everyday drivers.

Benefit: This gives athletes, cyclists, and everyday users far more precise and effortless speed and distance data than manual timing methods, removing sources of human error such as reaction time. It supports training, and safety features such as automatically alerting emergency services with a precise location if a cyclist stops moving unexpectedly after a fall.

Concern: Continuously recording a person's exact location and speed raises privacy concerns — this data reveals detailed patterns about where a person lives, works, and travels, and when. If stored by a company, shared with third parties, or accessed without permission, it could be misused to track someone's movements without their consent — which is why data-protection regulations increasingly require apps to be transparent and obtain clear consent before recording or sharing movement data.

Formula: $$ a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t} $$

Substitute: $$ a = \frac{20 - 0}{8} $$

Answer: $a = 2.5\,\text{m/s}^2$

The negative sign shows the cyclist is slowing down (decelerating) — the magnitude of the deceleration is $2\,\text{m/s}^2$.

Benefit: For the same change in speed (e.g. stopping from $15\,\text{m/s}$ to $0$), increasing the time taken to stop reduces the size of the deceleration, since $a = \dfrac{\Delta v}{\Delta t}$ — a larger $\Delta t$ gives a smaller $a$. Smaller decelerations mean smaller forces act on the occupants during the crash, significantly reducing the risk of serious injury compared to a rigid car that stops almost instantly.

Drawback: Crumple zones are designed to be permanently damaged in a collision, so even a moderate crash can be very expensive to repair or can write off the car entirely. Designing and manufacturing more complex crash structures can also increase the overall cost and weight of the vehicle.

Benefit: Precise acceleration data lets coaches pinpoint exactly where in the race an athlete loses time (for example, a slower-than-average acceleration phase out of the blocks) far more accurately than watching by eye. This allows training to be targeted efficiently, helping athletes improve performance and pursue faster times.

Drawback: This equipment, and the expertise needed to interpret its data, can be expensive, so athletes and teams with more funding have access to more precise training feedback than others. This could widen the performance gap between well-funded and under-funded athletes or countries, rather than the sport remaining a level playing field.

Benefit: Greater acceleration is a genuine safety and performance advantage in some situations — for example, accelerating quickly onto a busy motorway from a slip road, or overtaking safely, can reduce the time spent in a dangerous position relative to other traffic. Combined with EVs producing no exhaust emissions, this delivers both a performance and an environmental improvement over petrol cars.

Concern: Very fast, near-silent acceleration in urban areas increases risk to pedestrians and cyclists, who often rely partly on engine noise to judge how quickly an approaching vehicle is moving — a much higher-than-expected acceleration from a car that sounds like it is barely moving could catch pedestrians off guard, especially children or visually impaired people. High accelerations, especially in heavier EVs (due to battery weight), also increase tyre wear, releasing more microplastic particles into the environment despite there being no exhaust emissions.

An object will remain at rest, or continue moving at a constant velocity (constant speed in a straight line), unless a resultant (unbalanced) force acts on it.

Contact force (e.g. friction, or a push): requires the two objects to be touching for the force to act. Non-contact force (e.g. gravity, or magnetism): acts between two objects even when they are not touching, across a gap.

Benefit: A seatbelt applies a restraining (backward) force to the passenger's body at the same time the car decelerates, preventing the passenger from continuing to travel forward into the windscreen or dashboard due to their own inertia. This significantly reduces the severity of injuries and saves many lives in collisions, which is why seatbelt use is legally required in most countries.

Drawback: Some passengers find seatbelts uncomfortable or restrictive on long journeys, and in rare cases (for example a vehicle submerged in water or on fire) a jammed seatbelt buckle can make it harder for a passenger to escape quickly. Specially designed harnesses and anchor points are also needed for very young children, adding cost and complexity for parents and vehicle manufacturers.

Benefit: Rockets built on this principle have allowed the launch of satellites providing GPS navigation, weather forecasting, global communications, and internet access to remote areas, as well as enabling scientific research (such as studying climate change from orbit) that is not possible from the ground — technology that huge numbers of people now depend on daily.

Drawback: Rocket launches are very expensive and use large amounts of fuel, releasing significant carbon dioxide and other emissions into the atmosphere. The growing number of launches has also left thousands of pieces of "space debris" (old rocket stages and satellite fragments) orbiting Earth at high speed, which pose a collision risk to working satellites and future spacecraft, including crewed missions.

Benefit: By legally requiring every new car to demonstrably limit the forces (and so the injury risk) experienced by occupants during a collision, these regulations have driven real, measurable improvements in car safety over recent decades, directly reducing deaths and serious injuries on the roads, and giving manufacturers a strong incentive to keep improving safety design rather than treating it as optional.

Concern: Designing, building, and crash-testing cars to meet these standards adds significant cost to vehicle development, which is often passed on to buyers — this can make new, safer cars less affordable, particularly in lower-income countries or communities, meaning the safety benefit is not shared equally. Older, second-hand cars that predate stricter standards also remain on the road for many years, so the safety gap between the newest and oldest vehicles can be large.

Friction is a contact force that acts between two surfaces (or between an object and a fluid such as air or water) in contact. It always opposes (acts against) the direction of relative motion (or attempted motion) between the surfaces.

(1) How rough or smooth the two surfaces are — rougher surfaces produce more friction. (2) How hard the surfaces are pressed together — a greater force pressing the surfaces together (e.g. a heavier object) produces more friction.

Benefit: Reducing air resistance directly reduces the driving force (and so fuel) needed to maintain speed, especially on motorways — lowering fuel costs for drivers and reducing the CO₂ and other emissions released per kilometre travelled, helping reduce vehicles' overall contribution to climate change and air pollution.

Drawback: Prioritising a streamlined shape can conflict with other practical needs — for example, delivery vans and trucks need large, boxy shapes to maximise the space available for cargo, and a more streamlined design may reduce this usable space. Achieving very streamlined shapes can also require expensive materials and specialist engineering/wind-tunnel testing, increasing the manufacturing cost of the vehicle.

Benefit: A good tread pattern significantly increases grip in wet conditions by clearing water from between the tyre and the road, reducing the risk of "aquaplaning" (where a layer of water lifts the tyre off the road, drastically reducing friction and control). This directly improves road safety, particularly for braking distances in rain.

Drawback: Tyres with a more aggressive tread designed for maximum grip typically also increase rolling friction/resistance with the road, meaning the engine has to work harder (using more fuel) to keep the car moving at a constant speed compared to smoother, low-resistance tyres. Tyre tread also wears down over time through friction, releasing small rubber/microplastic particles into the environment and requiring tyres to be replaced periodically, adding cost and waste.

Benefit: Lighter, more compact parachute systems take up less mass and space, which is especially valuable in spacecraft (where every kilogram of payload is extremely expensive to launch), and stronger, more reliable fabrics reduce the risk of parachute failure — giving a safer, more controlled and predictable terminal velocity for landing astronauts, cargo, or Mars rovers safely.

Concern: This advanced fabric technology, and the engineering and testing needed to certify a parachute system as safe, is very expensive, meaning access to the most reliable, cutting-edge parachute systems tends to be limited to well-funded space agencies and companies rather than being available to all. A parachute is also a single point of failure in situations like spacecraft re-entry — if a small manufacturing fault or unexpected tear affects the fabric's strength, the consequences of a malfunction at the extreme speeds and heights involved (failing to reach a safe terminal velocity in time) can be catastrophic, so extremely rigorous (and costly) testing is essential.