العلوم
Acceleration: Change of Velocity, Divided by Time
Acceleration is change in velocity divided by time, in metres per second squared. Worked for a car, for braking, and for a car turning at a steady speed.
Acceleration
Acceleration is the rate of change of velocity — the change in velocity divided by the time it takes — measured in metres per second squared.
- أين يقابله الطلاب
- Grade 8 science, and again at GCSE and IGCSE in motion graphs and in the equation v² − u² = 2 a s.
الإجابة باختصار
Acceleration is the rate at which velocity changes: the change in velocity divided by the time taken, measured in metres per second squared. A car reaching 27 m/s from rest in 9 seconds is accelerating at 3 m/s². Slowing down counts, and so does changing direction, because velocity carries a direction.
مثال
a = (v − u) ÷ t = (27 − 0) ÷ 9 = 3 m/s²
The car starts at rest, so u is 0. It reaches 27 m/s after 9 seconds, so the velocity has changed by 27 m/s and the change took 9 seconds. Dividing gives 3, and the unit follows from the working: metres per second, divided by seconds. In plain words, the car is gaining 3 m/s of speed in every second that passes — after one second it is doing 3 m/s, after two 6 m/s, after three 9 m/s.
Metres per second per second is not a typo
The unit says exactly what the quantity is. Velocity is measured in metres per second; acceleration asks how fast that figure is changing, so it is metres per second, per second, written m/s². The squared sign belongs to the seconds, never to the metres.
Students who read m/s² as a kind of speed then find every question confusing, because a value of 3 m/s² does not tell you how fast anything is going. It tells you how quickly the speedometer needle is moving. A lorry at 3 m/s² is gaining speed faster than a sports car at 2 m/s², whatever speeds the two are currently doing.
Three ways to accelerate, and two of them surprise people
Everyday speech uses accelerate to mean speed up. Physics uses it for any change of velocity at all, which admits two more cases.
Slowing down gives a negative value. A car going from 20 m/s to rest in 4 seconds has a change of velocity of −20 m/s over 4 seconds, so its acceleration is −5 m/s². Writing this as a deceleration of 5 m/s² says the same thing; the minus sign is doing the work of the word.
The third case is the one that has to be taken on trust at first. A car going round a roundabout at a steady 30 km/h has a velocity pointing in a new direction at every moment, so it is accelerating the whole way round even though the speedometer never moves.
- Speeding up — velocity increases, acceleration positive
- Slowing down — velocity decreases, acceleration negative: (0 − 20) ÷ 4 = −5 m/s²
- Turning at a constant speed — the size of the velocity is unchanged but its direction is not, so the car going round a roundabout at a steady 30 km/h is accelerating the whole way round
Where it lives on a graph
On a velocity–time graph, acceleration is the gradient. A straight sloping line means the acceleration is constant, a steeper line means a larger acceleration, and a horizontal line means zero acceleration — which is not the same as zero speed, and a horizontal line high up the axis is a fast object that is simply not changing.
The area underneath that same graph is a different quantity again: it gives the distance travelled. Two questions about one graph, answered by two different operations, is where most of the marks in this topic sit.
أسئلة شائعة
Is deceleration the same as negative acceleration?
Yes, in ordinary use. Deceleration is the word for an acceleration that acts against the direction of travel, and in a calculation it comes out as a negative number. Write either, but be consistent: reporting an answer as a deceleration of −5 m/s² says the object is speeding up, which is usually not what was meant.
Can something accelerate while its speed stays the same?
Yes, if it is changing direction. Velocity has both a size and a direction, so a satellite in a circular orbit or a car on a roundabout at a steady speed is accelerating continuously, because the direction of its velocity is changing every moment. Speed alone is not enough to settle the question.
What is 9.8 m/s²?
It is the acceleration of an object falling freely near the Earth's surface, when air resistance can be ignored. Every second of the fall adds about 9.8 m/s to the downward speed, regardless of the object's mass. Many textbooks round it to 10 m/s² to make the arithmetic quicker; check which value your paper expects.
How is acceleration different from velocity?
Velocity says how fast and in which direction something is moving right now. Acceleration says how quickly that is changing. An object can have a large velocity and zero acceleration — a train at a steady 40 m/s — or zero velocity and a large acceleration, which is exactly the situation of a ball at the top of its bounce.
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