Almost every mechanics question starts by describing how something is moving, so the three quantities that describe motion — speed, velocity and acceleration — need to be separated properly before anything else. They are routinely treated as loose synonyms in ordinary speech, and the tests exploit that directly: a question will describe an object moving at a perfectly steady speed and then ask about its acceleration, and the answer is not always zero.
Speed
Speed is how much distance you cover in how much time, and nothing more. Divide the distance travelled by the time it took and you have it.
Speed
- how far it travelled, in metres (m)
- how long it took, in seconds (s)
The unit follows from the formula: metres divided by seconds gives metres per second. What that number describes is an average over whatever interval you measured — if a journey took an hour and covered sixty kilometres, the average speed was sixty kilometres per hour whether the trip was smooth or full of stops. When a question wants the speed at one particular instant rather than across an interval it will say so, usually with a word like "instantaneous" or by describing a speedometer reading.
Average speed and speed right now
The distinction between an average and an instantaneous value causes more trouble than it should. Average speed is total distance divided by total time, and it deliberately flattens everything that happened in between — a journey of 90 kilometres in one and a half hours has an average speed of 60 kilometres per hour whether it was driven at a constant 60 or spent half the time at 90 and half stationary in traffic. Instantaneous speed is what a speedometer shows: the speed over an interval so short that it has not had time to change. Questions signal which one they want, usually by describing a whole journey for the average and a single moment for the instantaneous, and the numbers are rarely the same.
One consequence worth noticing is that you cannot average two speeds by averaging the numbers unless the object spent equal times at each. Drive 30 kilometres at 30 km/h and another 30 kilometres at 60 km/h and the average speed is not 45 km/h, because the slow half took twice as long — the total is 60 kilometres in one and a half hours, giving 40 km/h. Whenever a question offers you the arithmetic mean of two speeds as an option, check whether the times or the distances were equal.
Velocity, and why the distinction matters
Velocity is speed with a direction attached. That sounds like a technicality and it is not, because it changes what counts as a change. An aircraft holding a steady 200 metres per second in a straight line has a constant speed and a constant velocity. Put it into a turn at the same 200 metres per second and the speed is still constant while the velocity is changing continuously, because the direction is changing even though the number is not. Since acceleration is defined as a change in velocity, that turning aircraft is accelerating — and this is exactly the trap the previous paragraph warned about.
Acceleration
Acceleration is how quickly velocity changes. Take the change in velocity and divide by the time the change took.
Acceleration
- acceleration, in metres per second squared (m/s²)
- the CHANGE in velocity — final minus initial — in metres per second (m/s)
- the time the change took, in seconds (s)
The Greek letter delta, written Δ, is standard shorthand for "the change in", so Δv means the final velocity minus the starting one and nothing more mysterious than that. If a car goes from rest to 30 metres per second, Δv is 30. If it goes from 30 down to 10, Δv is −20, and the negative sign is meaningful: it says the acceleration points opposite to the motion, which is what braking is. There is no separate quantity called deceleration in physics — there is only negative acceleration, and treating slowing down as a special case rather than a sign is a reliable way to get a question wrong.
Reading motion off a graph
Two graph types come up, and confusing them is common. On a distance–time graph, the slope is the speed: a steeper line means faster, a horizontal line means stopped. On a velocity–time graph, the slope is the acceleration instead — and the area beneath the line gives the distance travelled. That second reading surprises people, but it follows from what area means: the height is a velocity and the width is a time, so multiplying them gives a distance, exactly as the speed formula rearranged.
A distance–time graph is the other one you will meet, and the two are easy to mix up because they look similar. There, the vertical axis is distance rather than velocity, so the slope gives the speed and a horizontal line means the object has stopped — not, as on a velocity–time graph, that it is moving steadily. A curve that gets steeper on a distance–time graph means the object is speeding up. Always read the vertical axis label before interpreting the shape, because the identical straight line means "constant speed" on one graph and "constant acceleration" on the other.
When the acceleration is steady
For motion where the acceleration does not change, one further relationship links speed, acceleration and distance without any mention of time. It is worth having because braking questions almost always give you a distance rather than a duration.
Constant acceleration
- final velocity, in metres per second (m/s)
- starting velocity, in metres per second (m/s)
- acceleration, in metres per second squared (m/s²) — negative when braking
- distance travelled during the change, in metres (m)
The v² and u² are the important detail. Because the speeds are squared, doubling your starting speed does not double the distance needed to stop — it quadruples it. That single fact explains why stopping distances grow so alarmingly with speed, and it comes back in the energy module, where it turns out to be the same observation wearing a different name.
Putting it to work
Why it matters in aviation
The insistence that velocity carries a direction is the reason aviation keeps several different speeds apart rather than talking about speed at all. The aircraft's velocity through the air, added as a vector to the wind's velocity, gives its velocity over the ground — which is why heading, the direction the aircraft is pointed, differs from track, the direction it actually moves, and why airspeed and groundspeed can differ by a wide margin on the same flight. Airspeed itself divides further: the indicated airspeed a pilot flies by comes from the pressure of air striking a probe, while true airspeed is the actual rate through the air mass, and the two separate as air density falls with altitude. Only groundspeed is any use for working out how long a leg will take.
Acceleration matters most on the takeoff roll, where the aircraft has a fixed length of runway in which to reach flying speed, and a decision speed part way along it beyond which the takeoff is continued rather than abandoned. That is a constant-acceleration problem stated with a distance rather than a duration, which is exactly the arrangement v² = u² + 2as is for.
What the test asks
The recurring trap is the one this lesson opened with: an object moving at constant speed around a curve is described, and the answer options invite you to say the acceleration is zero. It is not, because the direction is changing. The second trap is treating braking as its own quantity rather than as a negative acceleration, which produces a sign error and a distance that comes out negative. The third is subtler — using the final velocity where the formula wants the change in velocity, which gives the right answer only when the object started from rest.