How do I use physics equations for this?

[netrunnr]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

what I did was this:
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 traveled is 30s
total distance traveled 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.

thanks for any advice offered.

 

[tiny-tim]

hi netrunnr!

what I did was this:
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

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

that is what physics equations are for!​

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

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 ​

 

[netrunnr]

hi netrunnr!


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

that is what physics equations are for!​

no, a = d/t is wrong
opps that is r = d/t my bad...


okay new take:
v = v₀+at

with these values for part I:
v =20m/s ; a = 2m/s² ; t = unknown
solve for t
20m/s = 0 + 2m/s²*t
20m/s * s²/2m = t
t₁ = 10s

values for part II:
v = 10m/s ; a =1m/s² ; t = unknown
10m/s = 0 + 1m/s² * t
`0m/s * s²/1m = t
t₂ = 20s

total time = t₁ + t_s = 30s

r = d/t solve for d
2m/s² = d₁/10s
2m/s²/10s = d₁
d₁=20m


1m/s² = d₂/20s
1m/s²/20s = d₂
d₂ =10m

total distance = d₁ + d₂ = 20m + 10m = 30m

let me know what you think and thanks for the help so far :)

 

[tiny-tim]

total time = t₁ + t_s = 30s

ok so far

r = d/t solve for d
2m/s² = d₁/10s
2m/s²/10s = d₁
d₁=20m


1m/s² = d₂/20s
1m/s²/20s = d₂
d₂ =10m

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

 

[netrunnr]

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

 

[tiny-tim]

(just got up :zzz: …)

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

a is for acceleration

 

[netrunnr]

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

 

[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:​

 

[netrunnr]

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

 

[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 = x_o + v_ot = 1/2at²
so part one is x₁=0 + 0 + 1/2*2*10² = 100m
then part 2 is x_total=100 + 20m/s+1/2*(-1)*20² = 300m

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

is this right?

 

[tiny-tim]

hi netrunnr!

I thought speed was acceleration...

ah, that explains a lot!

i was getting worried! ​

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

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! ​