IB Physics HLTopic 1 — Motion, Forces & EnergyPaper 1 & 2Change in velocity~7 min read
Acceleration
Velocity tells you how fast and which way; acceleration tells you how quickly that’s changing. Press the accelerator and you speed up; hit the brakes and you slow down — both are acceleration, just with opposite signs. And because velocity is a vector, even changing direction at a steady speed counts as accelerating.
📘 What you need to know
Acceleration is the rate of change of velocity — a vector, measured in m s−2
It’s found from a = Δv ÷ Δt, the velocity change over the time taken
Change in velocity is final − initial: Δv = v − u
Positive acceleration = speeding up; negative = slowing down (deceleration)
Acceleration can also be negative simply because it points in the negative direction
Instantaneous acceleration is the value at a single moment (a curved velocity–time graph)
Defining acceleration
Acceleration is defined as the rate of change of velocity. It’s a vector quantity, measured in metres per second squared (m s−2) — it tells you how much an object’s velocity changes every second. The average acceleration comes straight from the change in velocity divided by the time it took.
Average accelerationa = Δv ÷ Δt = (v − u) ÷ Δt
Here a is the acceleration (m s−2), v is the final velocity, u is the initial velocity, and Δt is the time taken (s). The change in velocity is always the final minus the initial: Δv = v − u.
The units are the clue to what acceleration really means. Metres per second squared is really (metres per second) per second — how many m s−1 of velocity you gain (or lose) each second. An acceleration of 2 m s−2 just means “2 m s−1 faster every second”. Say it that way once and the squared second stops looking mysterious.
Positive, negative & deceleration
The sign of acceleration carries meaning. If an object is speeding up, its acceleration is positive; if it’s slowing down, the acceleration is negative — often called deceleration. On a velocity–time graph, that’s the difference between a line sloping up and a line sloping down.
On a velocity–time graph, an upward slope is positive acceleration; a downward slope is negative acceleration (deceleration).
There’s a subtlety worth pinning down: a negative acceleration doesn’t always mean slowing down. Acceleration can be negative simply because it points in the negative direction. An object speeding up while travelling in the negative direction has a negative acceleration too — so read the scenario, not just the sign.
speeding up
→ sign →
+ acceleration
slowing down
→ sign →
− acceleration
Quick recap: acceleration = (final − initial velocity) ÷ time. A negative answer usually means deceleration — but can also just mean the motion is in the negative direction.
Instantaneous acceleration
Just like velocity, acceleration has an instantaneous value — the acceleration at a single point in time rather than averaged over an interval. If an object’s acceleration is itself changing, its velocity–time graph is a curve, and the instantaneous acceleration is the gradient of the tangent at that moment.
WE 1
A train decelerates uniformly in a straight line, its velocity dropping from 45 m s−1 to 36 m s−1 in 25 s. Find (a) the change in velocity and (b) the acceleration, and explain how the answer shows it’s slowing.
Part (a) — change in velocity
Δv = v − u
Δv = 36 − 45 = −9 m s⁻¹Part (b) — acceleration
a = Δv ÷ Δt
a = −9 ÷ 25 = −0.36 m s⁻²a = −0.36 m s⁻²The negative sign shows the train is decelerating — losing 0.36 m s⁻¹ of velocity each second.
WE 2
A car pulls away from a junction, its velocity rising from 8 m s−1 to 20 m s−1 in 6 s. Calculate its acceleration.
Change in velocity firstΔv = 20 − 8 = +12 m s⁻¹Then divide by the time
a = Δv ÷ Δt
a = 12 ÷ 6 = +2.0 m s⁻²a = +2.0 m s⁻²Positive → the car gains 2 m s⁻¹ of velocity every second as it speeds up.
💡 Top tips
Remember the units mean “per second, per second” — m s−2 is how much the velocity (in m s−1) changes each second.
Always do final minus initial for Δv — getting these the wrong way round flips the sign.
Keep the sign in your answer — it tells the examiner whether the object speeds up, slows down, or moves the other way.
Direction can be chosen — just be consistent about which way is positive throughout a problem.
⚠ Common mistakes
Computing Δv as initial minus final, flipping the sign
Assuming a negative acceleration always means slowing — it can mean motion in the negative direction
Dropping the minus sign and losing the “deceleration” mark
Muddling the units — writing m s−1 instead of m s−2 for acceleration
Up next: Kinematic Equations — the four “SUVAT” equations that tie displacement, velocity, acceleration and time together, letting you solve any constant-acceleration problem once you know three of the five quantities.
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