(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a vehicle starts from rest and accelerates at a reate of 2.0m/s^{2}in a straight line til it reaches a speed of 20m/s. then it slows to constant 1.0m/s^{2}til it stops.

how much time elapses from start to stop?

how far does the vehicle go?

2. Relevant equations

I have:

a_{1}= 2.0m/s^{2}

a_{2}= 1.0m/s^{2}

v_{1}= 2.0m/2

v_{2}= 0.0m/2

3. The attempt at a solution

what I did was this:

t_{1}=0s then 2m/s^{2}* 0s= 0

t_{1}=1s then 2m/s^{2}* 1s = 2m/s

t_{1}=10s then 2m/s^{2}* 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

t_{2}=0 then 1m/s^{2}* 0s = 0

t_{2}=1 then 1m/s^{2}* 1s = 1m/s

t_{2}=20 then 1m/s^{2}* 20s = 20m/s

now I have:

total time: t_{2}+ t_{1}= 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: d_{1}= 2.0m/s * 10s = 20m

d_{2}= 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.

thanks for any advice offered.

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# How do I use physics equations for this?

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