Math Help Forum: Rate of Velocity

Hello,

I'm having some difficulty figuring out how to go about doing this question. I don't have any graph examples in my notes, so I'm a bit confused. Here's the questions:

'Graphs of the velocity functions of two particles are shown, where t is measured in seconds. When is each particle speeding up? When is it slowing down?'



These are the two graphs. I'm just not sure how to read them...For the first one I guessed that it was speeding up at (0,0) but only the x-int was 0...

Thanks for any help!

Originally Posted by dark-ryder341

Hello,

I'm having some difficulty figuring out how to go about doing this question. I don't have any graph examples in my notes, so I'm a bit confused. Here's the questions:

'Graphs of the velocity functions of two particles are shown, where t is measured in seconds. When is each particle speeding up? When is it slowing down?'



These are the two graphs. I'm just not sure how to read them...For the first one I guessed that it was speeding up at (0,0) but only the x-int was 0...

Thanks for any help!

The trick here is in the fact that velocity involves direction and speed, not just speed. So when is something getting faster? When the sign of acceleration matches the sign of the velocity. For instance,

If something is moving with velocity 1, and builds up to velocity of 5, then it is clearly speeding up right? That's because acceleration is positive AND velocity is positive.

Now let's say its at 5 and goes to 1. Then it's slowing down. This is because velocity is positive and acceleration is negative.

Now let's say velocity is -1 and it goes to -5. This means it went from 1 to 5 in the opposite direction. Speed doesn't care about direction, so the object is speeding up. This is because velocity is negative AND acceleration is negative

And finally, if it has a velocity of -5 and moves to -1, it is slowing down. It was going 5 m/s in a direction and now it's going 1 m/s. Velocity is negative AND acceleration is positive. Thus it's slowing down


You should now be able to answer your question. In terms of calculus, you look at the graph to see if its above or below the t-axis and then look at the slope of the graph to see if acceleration (the derivative of velocity) is positive or negative.

If acceleration and velocity have the same sign, the object is speeding up

...except there's no graph of acceleration given.

@ OP: Though he was right. Speed is independent of direction. The steeper the slope (at the end of the interval given), then the faster the "object" is moving at that point.

It's a little subtle on these graphs, but the farther the velocity graph moves from the x axis, the faster it's going. Both of these are about the same at t = 4. But there's a little hook on one of them, implying that it's leveling out.

Keep the post in mind above for if you ever get a graph with acceleration and velocity (which you're probably more likely to get in Physics, but eh).

Originally Posted by Open that Hampster!

...except there's no graph of acceleration given.

@ OP: Though he was right. Speed is independent of direction. The steeper the slope (at the end of the interval given), then the faster the "object" is moving at that point.

It's a little subtle on these graphs, but the farther the velocity graph moves from the x axis, the faster it's going. Both of these are about the same at t = 4. But there's a little hook on one of them, implying that it's leveling out.

Keep the post in mind above for if you ever get a graph with acceleration and velocity (which you're probably more likely to get in Physics, but eh).

This is posted in calculus... meaning you're probably supposed to realize that acceleration is the slope of the velocity graph

So to find the sign of acceleration you just look at the velocity graph.... in this sense the graph serves 2 purposes

If the slope of the velocity graph is positive, then the sign of acceleration is positive and vice versa

Originally Posted by artvandalay11

This is posted in calculus... meaning you're probably supposed to realize that acceleration is the slope of the velocity graph

So to find the sign of acceleration you just look at the velocity graph.... in this sense the graph serves 2 purposes

If the slope of the velocity graph is positive, then the sign of acceleration is positive and vice versa

"Supposed to"

I'm not saying you're method is wrong, or even that what I wrote is better. It's just a more intuitive way to look at the problem.