# How do I use physics equations for this?

1. Feb 2, 2012

### netrunnr

1. The problem statement, all variables and given/known data

a vehicle starts from rest and accelerates at a reate of 2.0m/s2 in a straight line til it reaches a speed of 20m/s. then it slows to constant 1.0m/s2 til it stops.
how much time elapses from start to stop?
how far does the vehicle go?

2. Relevant equations
I have:
a1 = 2.0m/s2
a2 = 1.0m/s2
v1 = 2.0m/2
v2 = 0.0m/2

3. The attempt at a solution

t1=0s then 2m/s2 * 0s= 0
t1=1s then 2m/s2 * 1s = 2m/s
t1=10s then 2m/s2 * 10s = 20m/s

that gives me 10 seconds later the vehicle gets to a = 20m/s

so now the same thing for slowing down setting my 20m/s to t=0 and working from there
t2=0 then 1m/s2 * 0s = 0
t2=1 then 1m/s2 * 1s = 1m/s
t2=20 then 1m/s2 * 20s = 20m/s

now I have:
total time: t2 + t1 = 20s + 10s = 30s

this is the only equation given that I know how to apply:
total distance: based on a = d/t set to solve for d so d = at
total distance: d1 = 2.0m/s * 10s = 20m
d2 = 1.0m/s * 20s = 20m
20m + 20m = 40m

total time travelled is 30s
total distance travelled is 40m

the problem is I did not use any of the basic equations I was given in my book for this. I am at a loss as to how to match my equations to my work...... and seeing as this is the first week of the semester I have a feeling this is going to come back to haunt me drastically in about 4 weeks.

2. Feb 2, 2012

### tiny-tim

hi netrunnr!
yes, that's correct, but using v = vo + at would have been a lot simpler and quicker …

that is what physics equations are for!
no, a = d/t is wrong

look up your constant acceleration equations, and choose one that seems appropriate to find the distance(s) …

show us what you get

3. Feb 2, 2012

4. Feb 2, 2012

### tiny-tim

ok so far
i don't understand any of this

is r meant to be speed? (if so, please use v, like everyone else )

you've written r = d/t (instead of a), but you've used the acceleration anyway

5. Feb 2, 2012

### netrunnr

Hmmm I seem to have my vocabulary messed up....
Would it be correct to say
a = distance/time?

Last edited: Feb 2, 2012
6. Feb 3, 2012

### tiny-tim

(just got up :zzz: …)
a is for acceleration

7. Feb 3, 2012

### netrunnr

So what exactly is the rate that distance divided by time gives? Is it not acceleration?

8. Feb 3, 2012

### tiny-tim

speed!!

that's why speed is measured in m/s !

(and of course, only if the acceleration is zero)

get some sleep! :zzz:​

9. Feb 3, 2012

### netrunnr

omg a *duh* moment indeed.
lesson here : do not overthink a solution

10. Feb 9, 2012

### netrunnr

just learned something very important today regarding this - and it was the source of my confusion here:
Speed is the rate of change of distance with time.
Velocity is the rate of change of displacement with time.

I thought speed was acceleration.... so on that note:

my problem is a total time of 30s
and the distance traveled is:
x = xo + vot = 1/2at2
so part one is x1=0 + 0 + 1/2*2*102 = 100m
then part 2 is xtotal=100 + 20m/s+1/2*(-1)*202 = 300m

so the total distance traveled is 300m! not 30.

is this right?

11. Feb 10, 2012

### tiny-tim

hi netrunnr!
ah, that explains a lot!

i was getting worried!
yes, that's fine!

(warning: in an exam, don't do two lines in one, as in your last line …

there's nothing wrong with it, but there's so much chance of making a silly mistake that it's not worth it )

btw, you can also get there without using t, by using v2 = u2 + 2as (twice) …

try it!