# What is the concept of per second per second? Like acceleration?

1. Feb 22, 2012

### jinkazama99

What is the concept of per second per second?? Like acceleration??

I'm in my final year of college and I'm struggling to get a clear idea on the concept of per second squared. I mean a meter per second yeah that's understandable, it's just mean your moving a meter per second, so 5 seconds later, you'll be 5 meters away from your starting point, but a meter per second per second? Can someone give me some examples please?? Thanks as usual

2. Feb 22, 2012

### Staff: Mentor

Re: What is the concept of per second per second?? Like acceleration??

Think of "meter per second per second" as "(meter per second) per second", not as "meter per (second per second)".

Acceleration is change in velocity (meters per second) in some amount of time (seconds). If at some point in time you're moving at 5 m/s, and then ten seconds later you're moving 25 m/s, then you've changed your velocity by 20 m/s in 10 s which gives an acceleration of 2 m/s per s, which we customarily write as 2 m/s2.

3. Feb 22, 2012

### phyzguy

Re: What is the concept of per second per second?? Like acceleration??

My brother tells a funny story about how when he first saw the phrase 10 meters per second per second he thought it was a typo.

I've found it helps some people to understand if you use different words. So an acceleration of 10 meters per second^2 means you velocity changes by 10 meters per second each second. Or think of an acceleration of (5 miles per hour) per second. This means you start motionless and 1 second later you are going at 5 miles per hour. Do these examples help?

4. Feb 22, 2012

### jinkazama99

Re: What is the concept of per second per second?? Like acceleration??

So let's say I start driving and when i reach point a, my speed is 50 m/s and it stays constant.

Case 1: 10 seconds later, I'm 500 meters away from point a, acceleration = 0.

Case 2: I accelerate by 70 m/s per second, 10 seconds later, I would've been 700 meters away from point a?

5. Feb 22, 2012

### jinkazama99

Re: What is the concept of per second per second?? Like acceleration??

That's great explaination phyzguy, I've find all these mathematic concepts always much easier to learn by real life examples!! I really like the idea of using each second as opposed to per second per second, my head just can't seem to cope with this type of sorcery!! I'll just go with per second each second from now on, you helped a great deal and I thank you again good sir!!

6. Feb 22, 2012

### Integral

Staff Emeritus
Re: What is the concept of per second per second?? Like acceleration??

Good
Not so good.

here is what you did $70 \frac m {s^2}$ X 10s = 700$\frac m s$

note that since I multiplied by seconds I was able to cancel only 1 second from the denominator. What you have is your speed after 10s not the distance traveled.

Distance is given by: $\frac 1 2$ a t2

7. Feb 22, 2012

### jinkazama99

Re: What is the concept of per second per second?? Like acceleration??

Ah I see now, I've just assumed since I'm increasing my speed by 70m per sec, 10 seconds later i would have to simply multiplty the 10 by 70 to get the distance, so stupid...

Thank you mentor, I'm quite clear on the acceleration and the meter squared concept now

8. Feb 22, 2012

### technician

Re: What is the concept of per second per second?? Like acceleration??

A good way to look at this is from a car salesmans perspective.
He will give the performance of a car perhaps as 'from 0 to 60 in 6 secs'
This means the car can accelerate from 0 to 60mph in 6 seconds.
In physics we might prefer to see this as 10mph per second
In fact we prefer to measure speeds in m/s so for us acceleration becomes metres/sec per sec.....m/s/s m/s^2

9. Feb 22, 2012

### gerechte23

Re: What is the concept of per second per second?? Like acceleration??

can someone help me to find an function Y of which Y'(0)=1/2, Y''(0)=1=2/2..
the nth derivative verifies Y''''''''(0)=n/2