Like if a car starts at rest and moves at 4m/s^2 for 10seconds, what does that mean?
Does it mean the car is exponentially increasing in speed? Can someone draw it out for me second by second?
Edit:
***I have a follow up question to several of y’all’s responses in how the concept of acceleration relates to one of the big kinematics equations as well. That’s one of the big discrepancies I’m having trouble understanding***
In: 9
I love to think of “per second” as a change.
Start with meters. Measure of where you are. Easy peasy idea.
Then, velocity. The change in meters. 1 meter per second means you are moving 1 meter every second. After 10 seconds, you’ll have gone 10 meters. Still good here.
Then, acceleration. The change in velocity. (1 meter per second) per second means your velocity is going up by 1 meter per second every second. So, if you accelerate (1 meter per second) per second, after 10 seconds, your velocity is 10 meters per second.
Don’t think of “meters” per “second per second”.
Think of “meters per second” per “second”.
An acceleration of 9.8 m/s2 means that every second, you can add an additional 9.8 m/s to your speed.
Your speed is going up 9.8 “meters per second” per “second.”
0 sec. 0 m/s
1 sec. 9.8
2 sec. 19.6
It’s crazy when it hits! But there are even crazier units out there. And they usually seem to “make sense”. Math is nuts!
So instead of seconds squared, think of it as an increase in (meters per second) per second. So every second its speed is increasing. That’s acceleration.
If you are going a constant speed, then if you draw a graph of your distance from the starting point, it would be a line at an angle, something like Y = X.
However, if you are accelerating, your distance from the starting part increases exponentially, like the right side of a parabola.
It’s a measure of change in speed over time.
It means that every second, the speed increases by 4 m/s.
At t=0s, car speed is 0 m/s
at t=1s the speed is 4 m/s
at t=2s speed is 8 m/s
at t=3s speed is 12 m/s
…
at t=10s speed will be 40 m/s
If the car is not accelerating (ie. speed is constant) then the speed will be the same at every point in time.
Think of it this way, speed is meters per second, ie the change in distance (m – unit of distance) over time (s).
Acceleration is change in speed (m/s – unit of speed) over time (s), so it’s (m/s)/s which then gets shortened to m/s^2
Don’t think of “meters” per “second per second”.
Think of “meters per second” per “second”.
An acceleration of 9.8 m/s2 means that every second, you can add an additional 9.8 m/s to your speed.
Your speed is going up 9.8 “meters per second” per “second.”
0 sec. 0 m/s
1 sec. 9.8
2 sec. 19.6
It’s crazy when it hits! But there are even crazier units out there. And they usually seem to “make sense”. Math is nuts!
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