# “Does that mean you’re increasing your speed 2.5 meters every second?” Acceleration formula

I saw a comment on a video on Youtube,

About acceleration. A teacher basically said that acceleration is Δv/Δt

He gave a situation where a person went from 5 m/s to 10 m/s and calculated the acceleration, assuming a constant acceleration.

Someone left this comment:

What does 2.5 actually represent?

Does that mean you’re increasing your speed 2.5 meters every second?

And how would this work with a non constant acceleration, since most acceleration isn’t constant?

A car takes longer to go from 60 to 100 than it does to go from 0 to 60. How does m/s^2 actually come into play in the real world?

If it can’t be used for the way cars accelerate then why does it matter?

Here is my response:

It’s written as 2.5 m/s^2, but it may make more sense to think about as being [ 2.5 m/s (units of velocity) per second ]. 2.5(m/s)/s.

That means that the person’s velocity increases by 2.5 m/s each second.

The acceleration is the rate of change of the velocity, how much the velocity changes in a given amount of time. You increase by the units of velocity, m/s, each s.

In a car, a constant acceleration will feel ‘smooth’. So that may be what you want to do as you drive.

Let’s say, you start a car, 0 m/s.

And let’s say you do accelerate at a constant 5 m/s.

You would be going 0 m/s
After 1s, 5 m/s
After 2s 10 m/s
After 3s 15 m/s

The constant acceleration will be more comfortable than a ‘jerky’ acceleration.

If you think about another equation in physics, KE = 1/2 m v^2, you’ll see that higher velocities require more energy. That is related to why you cannot accelerate as quickly from 60 to 100 compared to 0 to 60. (I’m assuming you mean mph or km/hour).

Much of the time in an early level physics classes, at least towards the beginning of the class, you mostly deal with constant accelerations.

It is easier to calculate.

But also, it can be useful, especially when you think about average velocities and average accelerations.

And in another common situation, the acceleration due to gravity is constant for many situations.

You can definitely deal with non-constant acceleration in physics, it involves calculus. I’m not sure what math/physics you are taking currently.