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Course: High school physics (DEPRECATED)>Unit 1

Lesson 5: Average and instantaneous acceleration

Acceleration review

Review the key concepts, equations, and common misconceptions related to acceleration.

Key terms

TermMeaning
Average accelerationRate at which velocity changes over a specified time interval. A vector quantity with SI units of $\frac{\text{m}}{{\text{s}}^{2}}$.
Instantaneous accelerationRate at which velocity changes at a specific instant in time. A vector quantity with SI units of $\frac{\text{m}}{{\text{s}}^{2}}$.

Equations

EquationSymbol breakdownMeaning in words
$\overline{a}=\frac{v-{v}_{0}}{t}=\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}$$\overline{a}$ is average acceleration, $\mathrm{\Delta }v$ is change in velocity, and $\mathrm{\Delta }t$ is change in timeAverage acceleration is the change in velocity divided by change in time.

Common mistakes and misconceptions

• People forget that an object can accelerate by changing direction. Velocity and acceleration are vector quantities, so they have both magnitude and direction. If the speed of an object remains the same but it changes direction, then the object is accelerating.
• People sometimes forget that acceleration and velocity aren’t always in the same direction. When velocity and acceleration vectors point in opposite directions, the object is slowing down.

For deeper explanations, see the video introducing acceleration.
For more on velocity vs. time graphs, see our article what are velocity vs. time graphs?.
To check your understanding and work toward mastering these concepts, check out our exercises on calculating average acceleration from graphs and connecting acceleration and velocity graphs.

Want to join the conversation?

• How can an object accelerate by changing direction?? Can you explain more clearly "If the speed of an object remains the same but it changes direction, then the object is accelerating"?
• Remember, velocity and acceleration are vector quantities, which have both magnitude and direction (+/-).

For example you are running east with an acceleration rate of k m/s^2. For every second you run, your speed/velocity increases by k. After a period of time, you then turn around 180 degree (we're talking about one dimensional motion) and head west instead. Now even though your speed stays the same, the next second you run, the acceleration is going to be -k as you are heading towards the opposite direction. Hope that helps.
• I have difficulty understanding this too.

"People forget that an object can accelerate by changing direction. Velocity and acceleration are vector quantities, so they have both magnitude and direction. If the speed of an object remains the same but it changes direction, then the object is accelerating."

If an object was traveling at a certain velocity and zero acceleration, then switched direction 180 degrees and continued in that direction at the same magnitude of velocity, how does that give acceleration?
• when you say same magnitude of velocity, that basically is speed. Instead of 180 degrees, lets say you turn 90 degrees and you continue at the same speed, same idea but easier to explain.
Initially, before turning, you are going straight at 5 m/s for example. But then you suddenly turn right 90 degrees and continue at 5 m/s. Here speed has remained constant while velocity has changed.
Velocity takes direction into account as well. So after turning right, as we were initially taking forwards as the direction, velocity is 0. This is because you are not going forwards anymore, you turning left. This results in a change in velocity, hence causing acceleration.
Here is an analogy which may help.
You are in a 100m race, and the track is straight. Let's say you travel 50m in 5 seconds. That is 10m/s. But for some reason, you turn right and run at 10 m/s. But because you are going right, you are not surpassing 50m in the race. You are in the same place as someone standing still at the 50m mark. Therefore your velocity is now 0m/s. The change from 10m/s to 0m/s is acceleration. (deceleration to be more precise)
• What's SI?
Standard Integration?
Super Integer?
• It's Systemme Internationale, French word for International System. Hope that helps!
• How do you express distance in terms of velocity and constant acceleration?
• How do you express distance in terms of velocity and constant acceleration?
• We aren't at this point in physics yet. Maybe at a later point.
• Despite rewatching the video many times and doing exercises I think I still have trouble connecting acceleration and velocity graphs. I think I do not fully grasp the concept of how they connect when forced to choose the one responding to the other. How to explain their connection differently than in these videos?
• If the graph is 20 m/s to the west, the cooresponding graph's y-intercept will be -20 m/s, and if the first graph's slope is positive, the cooresponding graph will also be positive. If the graph is positive with a constant acceleration, the cooresponding graph will be a straight line on the positive side, and vice versa.
• what is the acceleration for the pointer movement on your computer??
• The computer screen cursor has no acceleration nor even movement. The computer checks how you have moved the computer mouse and redraws the cursor in the appropriate location on the screen. This happens so quickly that it gives the appearance that the cursor is moving, though in reality, it is simply appearing in a new location without movement.
• If slowing down is negative acceleration, how do you describe the direction of acceleration.
• Acceleration is a vector quantity. This means that you include direction while describing acceleration. Slowing down means that you are decreasing your velocity, which means there is a negative change in velocity and therefore a negative acceleration. For example, if I was running to the right and my velocity went from 5 m/s to 2 m/s in 3 seconds, my acceleration would be -3 m/s^2, or 3 m/s^2 to the left. The negative sign basically means that it is going to the left.