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
This means the car is quadratically increasing in its *position*. In this case it probably makes the most sense to visualize it as something like a drag race, where time = 0 at the start of the race and position = 0 at the starting line.
Taking a unit “per second” allows you to describe the rate of change of that unit. At a given point in time, we can describe the position of the car in meters past the starting line. If we want to describe the rate at which the position is changing, we can describe a speed in meters per second. That is to say, if the speed is 4 m/s, then the car’s position increases by 4 for every second that elapses. If the car travels at 4 m/s for 10 seconds, then the car’s position will have increased by a total of 40 meters.
Describing movement as “increasing position” is kinda weird but it allows us to make the extrapolation to acceleration much easier.
However, the speed of the car is not constant. We know this because the car is stationary at the start, and moving at the finish line, so the speed changes over the duration. The rate at which the speed changes is what we call acceleration. If we want to describe the rate at which the speed is changing, we can use meters per second per second, which is the same as meters per second squared. That is to say if the car’s acceleration is 4 m/s^2, then the car’s speed increases by 4 m/s for every second that elapses. If the car accelerates at 4 m/s^2 for 10 seconds, then the car’s speed will have increased by 40 m/s.
Now if you want to know how far a car which starts stationary and accelerates at 4 m/s^2 for 10 seconds has gone, then you need to have a bit of an understanding of basic calculus. However, in this case it comes out to be 1/2 * 4 * 10^2 = 200 meters.
Seconds squared is second per second.
Ie I’m accelerating at 2 m/s/s or 2 m/s^2 or 2 m per second per second.
T = 0 seconds, velocity is 0 m/s.
T= 1 s, v is 2 m/s
T = 2 s , v is 4 m/s
Etc.
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.
It’s a lot easier to think of it as meters per second, per second. Because m/s /s = m/(s*s) = m/s^2
If you think of it as meters per second, per second, you can see how a car’s velocity can change by 3 meters per second, per second of time passed.
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
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.
Velocity is meters per second.
Acceleration is the change in velocity per second or (meters per second) per second.
So…
(m/s)/s = (m/s) * (1/s) = m/(s*s) = m/s^2
This means the car is quadratically increasing in its *position*. In this case it probably makes the most sense to visualize it as something like a drag race, where time = 0 at the start of the race and position = 0 at the starting line.
Taking a unit “per second” allows you to describe the rate of change of that unit. At a given point in time, we can describe the position of the car in meters past the starting line. If we want to describe the rate at which the position is changing, we can describe a speed in meters per second. That is to say, if the speed is 4 m/s, then the car’s position increases by 4 for every second that elapses. If the car travels at 4 m/s for 10 seconds, then the car’s position will have increased by a total of 40 meters.
Describing movement as “increasing position” is kinda weird but it allows us to make the extrapolation to acceleration much easier.
However, the speed of the car is not constant. We know this because the car is stationary at the start, and moving at the finish line, so the speed changes over the duration. The rate at which the speed changes is what we call acceleration. If we want to describe the rate at which the speed is changing, we can use meters per second per second, which is the same as meters per second squared. That is to say if the car’s acceleration is 4 m/s^2, then the car’s speed increases by 4 m/s for every second that elapses. If the car accelerates at 4 m/s^2 for 10 seconds, then the car’s speed will have increased by 40 m/s.
Now if you want to know how far a car which starts stationary and accelerates at 4 m/s^2 for 10 seconds has gone, then you need to have a bit of an understanding of basic calculus. However, in this case it comes out to be 1/2 * 4 * 10^2 = 200 meters.
Acceleration measures how fast velocity or speed are changing (velocity is speed in a certain direction, speed doesn’t care about direction).
In your specific example, the car’s acceleration is increasing its speed by 4metres per second every second.
As you noted it starts from rest, this means after 1 second it is moving at 4m/s, after 2 seconds it’s moving at 8m/s and so on up to the 10 second mark where it is moving at 40m/s.
Acceleration measures how fast velocity or speed are changing (velocity is speed in a certain direction, speed doesn’t care about direction).
In your specific example, the car’s acceleration is increasing its speed by 4metres per second every second.
As you noted it starts from rest, this means after 1 second it is moving at 4m/s, after 2 seconds it’s moving at 8m/s and so on up to the 10 second mark where it is moving at 40m/s.
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