The position-time “p-t” graph is one that gets used a lot, and since it's axes are position and time, the slope of the line will give average velocity to describe the motion of an object. If the velocity is constant, then the slope is constant and you'll see a straight line (either uphill or downhill). If velocity is changing, you'll see a curved rather than straight line for the slope. A steeper line indicates larger velocity. An uphill slope means positive velocity, downhill indicates negative velocity. If the slope is downhill and curved, but it starts out like a skier on a bunny hill, then the negative velocity starts slow and moves fast as time goes on, which is a sign of negative acceleration (starting slow and speeding up). If the slope looks instead like starting at the top of a black diamond run, then the object starts with a high negative velocity but ends with a slower velocity, a indication of positive acceleration.
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We need to keep in mind that acceleration can be an increase or a decrease. Yes indeed, the velocities in the table are all positive. However, the velocities are decreasing over time. A decrease in velocity is a negative acceleration.
At 9:38 in the video, you say the velocity vector is negative. However, the values in the table for velocity are all positive, which means the position is continuing to increase in the positive direction. Did you mean to say the acceleration vector is negative because the object is slowing down, but the velocity vector is still positive?
Good question. We have to lay a coordinate system (a grid) down in order to talk about plus and minus signs. On the p-t graph, for a straight line, this means that there’s no change in velocity. Slope of any graph = rise / run, so in our position-time graph, that number is velocity. Velocity is a number plus a direction, so if positive is north on our grid, then if your car is going 55 mph south, it will be shown as -55 mph.
For acceleration, on a p-t graph, if you see a curve, it means that the slope is changing, the “steepness” is changing, which corresponds to the velocity changing. A positive sign in front of that acceleration number at a specific point means at that time, the velocity is increasing, so the steepness increases. Work through more of the videos as we go through several examples together!
The comment about the negative sign in front of a number not corresponding to direction is very confusing. It would be great if this video had several more examples because the one with negative acceleration didn’t quite get the idea into my mind.
I would have like to see actual examples mapped for positive and negative acceleration that start high on the y-axis and go to lower y values as time increases. It was not clear to me what those graphs represent differently- is it an object moving in the opposite direction?
Nothing to print out – just come along and enjoy the ride! The email went out today for everyone.
What page do we print out for this lesson?