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    Acceleration Calculator (a = Δv/t)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find acceleration, change in velocity or time using a = Δv ÷ t. Enter a negative change in velocity for something slowing down.

    Quick answer

    Acceleration = change in velocity ÷ time taken. Use m/s and seconds to get m/s². For example, 0 to 24 m/s in 8 s gives 24 ÷ 8 = 3.0 m/s². Slowing down gives a negative acceleration (a deceleration).

    By Engr. Mehmood Kakar · Updated

    a = Δv ÷ t
    Find:

    Δv = final velocity − initial velocity. It is negative if the object slows down.

    Simulation

    Change of velocity over time

    Set the starting and final velocity and the time taken. The speedometer swings across and the velocity–time graph shows the acceleration as its gradient.

    0 m/s
    24 m/s
    8 s

    If the final velocity is less than the starting velocity, Δv is negative and so is the acceleration: the object is decelerating.

    Put these numbers in the calculator above

    How to calculate acceleration

    Acceleration is how quickly velocity changes. It is the change in velocity divided by the time taken:

    acceleration = change in velocity ÷ time taken

    • a is acceleration in metres per second squared (m/s²)
    • Δv is the change in velocity, final − initial, in m/s
    • t is time in seconds (s)

    A car that goes from rest to 24 m/s in 8 s has an acceleration of 24 ÷ 8 = 3.0 m/s². Every second, its velocity goes up by 3 m/s.

    When something slows down, the change in velocity is negative, so the acceleration is negative. That is a deceleration. A cyclist braking from 20 m/s to rest in 4 s has Δv = −20 m/s and a = −5.0 m/s².

    On a velocity–time graph, the acceleration is the gradient. For uniform acceleration over a distance, use v² − u² = 2as instead.

    Common mistakes that cost marks

    1. Using the final velocity instead of the change. Δv = final − initial. From 10 to 30 m/s, Δv is 20 m/s.
    2. Not converting km/h. 108 km/h is 30 m/s. Divide by 3.6.
    3. Writing the unit as m/s. Acceleration is in m/s², metres per second per second.
    4. Dropping the minus sign when slowing down. A deceleration has a negative acceleration.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A car accelerates from rest to 24 m/s in 8.0 s. Calculate its acceleration.[2 marks]
    1. a = Δv ÷ t
    2. a = (24 − 0) ÷ 8.0
    3. a = 3.0 m/s²
    Q2A train accelerates at 2.5 m/s² for 6.0 s. Calculate its change in velocity.[2 marks]
    1. Rearrange: Δv = a × t
    2. Δv = 2.5 × 6.0
    3. Δv = 15 m/s
    Q3A car reaches 108 km/h from rest in 10 s. Calculate its acceleration in m/s².[3 marks]
    1. Convert: 108 ÷ 3.6 = 30 m/s
    2. a = Δv ÷ t = 30 ÷ 10
    3. a = 3.0 m/s²

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for acceleration?

    Acceleration = change in velocity ÷ time taken (a = Δv/t). Acceleration is in m/s², velocity in m/s and time in s.

    What does a negative acceleration mean?

    The object is slowing down. A negative acceleration is called a deceleration.

    How do you find acceleration from a velocity–time graph?

    Acceleration is the gradient of the graph: the change in velocity divided by the change in time.

    Why is acceleration in m/s²?

    It is a change in velocity (m/s) every second, so metres per second per second, written m/s².