somebody explain the idea of acceleration units to me. The whole “seconds squared” or “seconds per second” makes no sense to me.

Question

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

Answer 1

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.