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## Differential Calculus

### Course: Differential Calculus > Unit 4

Lesson 2: Straight-line motion- Introduction to one-dimensional motion with calculus
- Interpreting direction of motion from position-time graph
- Interpreting direction of motion from velocity-time graph
- Interpreting change in speed from velocity-time graph
- Interpret motion graphs
- Worked example: Motion problems with derivatives
- Motion problems (differential calc)
- Total distance traveled with derivatives

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# Interpreting direction of motion from velocity-time graph

Given the velocity-time graph of a linear motion, we can interpret whether the moving object moves forward or backward (or right or left, depending on how we define the motion!).

## Want to join the conversation?

- I am having a bit of trouble understanding this. In your previous vid before this when X was 0 you said it was "forward" whereas in this vid it seems to be "neither". Anyone have an explanation for this?(5 votes)
- These videos are using different graphs. The first video was a graph of
*position*versus time, and the object was moving forward because the slope of the tangent line at that point was positive - a moment later, the object will have moved forward. This video is aboutversus time, and the velocity at x=0 is -4 (according to the graph), so this means that the particle is moving backwards. Tell me if you need any more help!**velocity**(12 votes)

- Is positive velocity always to the right and negative to the left?(3 votes)
- No, we can define positive/negative to correspond to either direction.(3 votes)

- Just curious what is the function of the graph?? (y=sinX) maybe?(2 votes)
- While you can't find the exact values, you can estimate them pretty well:

https://www.desmos.com/calculator/ii546med0q(3 votes)

- Would you still be moving forward if the point was
*(5, 2.5)*? Would it be backward for*(6.5, -2)*?(2 votes)- Exactly right. Let's look at 6,0. Since this is a velocity graph that means there is no speed. A moment before, even at 5.9999999, it was slightly negative, so up until 6 seconds the movement was backwards. Then, right after 6 seconds it is moving forward.

As it increases or decreases that just means the forwrd or backwards speed is increasing/ decreasing. As long as the line is above the x axis it is moving forward and as long as it is below it is moving backwards. Keep in mind this is just for a velocity graph.(3 votes)

- In the practice set, I use the rule that he said at0:28. However, sometimes when I use the fact that the velocity is negative and count it as going backward or I say that it's neither when the velocity is 0, it says my answer is wrong. Why is this?(1 vote)
- For the point at1:17, what would it look like if an object is "still moving backwards" but less than before?(1 vote)
- I try to visualise for you an example, not fully corresponding to reality but makes the mental picture. Say we have a basket ball and we start at point 2 seconds on Sal's graph where velocity is zero (cut out the previous part). We throw the ball up in the air. Do you see how the ball reaches its peak hight at 6 seconds where the velocity reaches zero and the ball is in standstill? Now try to reverse that idea for the second part of the graph starting from the 6 seconds. Think of it like throwing the basketball into water, 10 would be the maximum depth before the basketball starts to shot back up. Now can you see how at 9 seconds the ball still has some velocity before reaching the standstill and maximum depth at 10 seconds? Hope that helps at least I tried to visualise it that way at it made sense.(1 vote)

- how do you know if it is right(1 vote)
- I'm glad I'm not the only one here in 2020(1 vote)

- what does negative velocity indicate?(1 vote)
- why does the velocity need to be positive to be moving forward and vis versa?(1 vote)

## Video transcript

- [Instructor] An object
is moving along a line. The following graph gives the
object's velocity over time. For each point on the graph, is the object moving forward,
backward, or neither? So pause this video and see
if you can figure that out. All right, now let's do this together. And so we can see these different points on this velocity-versus-time graph. And the important thing to realize is is if the velocity is
positive, we're moving forward. If the velocity is negative,
we're moving backward. And if the velocity is
zero, we're not moving either forward nor backwards, or neither forward nor backwards. So right over here we see that our velocity is positive. It's a positive two meters per second. So that means that we are moving forward. Now, over here our velocity
is zero meters per second. So this is neither. Now, over here our velocity is negative four meters per second. So one way to think about it is we're moving four
meters per second backward. So I'll write backward. Now, this is interesting, this last point. 'Cause you might be tempted to say all right, I'm oscillating. I'm going up. Then I'm going down. Then I'm going back up. Maybe I'm moving forward here. But remember, what we're
thinking about here, this isn't position versus time. This is velocity versus time. So if our velocity is negative,
we're moving backwards. And here our velocity is still negative. It's becoming less negative,
but it's still negative. So we are still moving, we are still moving backward. If we were at this point right
over here or at this point, then we would be moving forward if our velocity were positive.