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### Course: Physics archive>Unit 1

Lesson 3: Acceleration

# Acceleration vs. time graphs

David explains how to read an acceleration vs. time graph. He then shows how the area under the curve gives the change in velocity and does a few examples. Created by David SantoPietro.

## Want to join the conversation?

• why v0 is equal to 1m/s?
• We didn't know what the initial velocity was, so he defines it . Now we know the change in velocity was 8 m/s (but not the actual velocity) and the initial velocity was 1 m/s. So at 4 seconds the velocity is 8 m/s(the change) + 1 m/s(initial) = 9 m/s or V4= 8 m/s + V0. V0 is defined as 1 m/s.
• why the acceleration at the 0 second is 1 m/s? shouldnt that be 2 m/s because the graph's line is horizontal. Isnt that means the acceleration is constant?
• You are correct that the horizontal graph means the acceleration is constant! But look at the units to help you. It is the acceleration that is constant at 2 m/s^2, not 2 m/s. At , what he says is that v = 1 m/s (velocity) at t = 0, this is the initial velocity of the dog. Since the dog accelerates at 2 m/s^2, the velocity will not be constant, but will increase. But there is no velocity graph in this video, only an acceleration graph.
• How come the velocity after 4 seconds isn't negative? Why is it higher at 6 seconds, and then decreases after the line moves into the fourth quadrant? From what I can understand, the acceleration was less at six seconds than it was at four seconds - the object was decelerating - so wouldn't that mean that by default the velocity was less?
(1 vote)
• I am very new to the physics scene, but I thought I might make an attempt to answer your question so that I can test my own knowledge. I'm sure one of the very helpful members of Khan Academy will approve/disprove my answer. So here goes...

Values above the horizontal (time) line represent positive acceleration (i.e. speeding up), while values below the line indicate negative acceleration (i.e. slowing down). This, of course, is based on the assumption that "Daisy the dog" is travelling in the direction where positive is forward (i.e. increasing in positive integers) and negative is a backward direction.

That being said, Daisy's velocity is greater at 6 seconds because the acceleration is positive (i.e. above the horizontal line), and is increasing at 2 m/s/s between 4 and 6 seconds. Therefore, she is speeding up.

I hope this helps, but more importantly, is correct! :)
• At , can you explain what does he mean
thanks
• He is just trying to tell that when we add up the area of all those small rectangles, their sum gives the area of the triangle. Therefore we need to find the area of the triangle.

Thus we must apply the area of triangle formula. Which is why we divide it by 2.

Hope that helps :)
• I don't get how velocity can be negative.
• It is only assuming,in the real,velocity cant be negative but for the problems solving its very useful.
As velocity is a vector quantity,it has a direction.
If I drive from my home to my workplace (and then defining my positive direction in that way), then my velocity is positive if I go to work, but negative when I go home from work. It is all about direction seen from how I defined my positive axis.
• What does negative acceleration mean? Does is mean that the object is slowing down?
• No, a negative acceleration just means that the acceleration is in the negative direction. If an object is traveling in the direction that is considered negative then a negative acceleration means that the object is getting faster. But if an object is traveling in the positive direction then a negative acceleration would mean that it is slowing down.
• Is jerk expressed as a distance per s^3, or how many meters per second per second an object gains in a second? Can a jerk graph in time be linear?
• Jerk is the time derivative of acceleration, which is meters per second per second, so you are entirely right! A jerk graph can certainly be linear; that would imply an acceleration which increases quadratically with time.
• How can we represent a body at rest on an acceleration vs time graph?
• You can only indicate velocity is constant in an acceleration vs time graph by having the graph be a flat line along the time axis so the acceleration is 0. On the graph you can't tell if the constant velocity is 0 or 1,000 m/s.