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

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.

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!

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.

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.

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