Simple acceleration quesiton

[sizillyd]

Ok here is the question. This seriously pissed me off for like 20 mins:

A particle starts from rest and travels in a straight line for 4 seconds. If the particle is accelerating at a constant rate, which of the following could be the distances traveled by the particle during each consecutive second?

A) 10m, 20m, 30m, 40m
B) 5m, 15m, 25m, 35m
C) 5m, 25m, 125m, 625m
D) 2m, 4m, 8m, 16m

The answer is B. The explanation seems like something from WAY out in left field. Can somebody explain this to me? Thanks a lot!

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[fizzgig]

they're being bastards. to my late night brain anyway. stupid first week physics crap tripping me up.

x = 1/2*at^2

plug in t=1 and the first x's, and get your accelerations

now use those accelerations and see what distance you should get at t=2

these are 40, 20, 20, 8, respectively. so distances should be
t=1 t=2
10 40
5 20
5 20
4 8

wtf, you say. they say distance traveled by the particle DURING EACH consecutive second. look the t=2 values you got are the distances traveled over the full 2 seconds. subtract distance traveled in the previous seconds to get the answer.

20-5 = 15 so only B has the correct first 2values.

 

[ElliottB]

The key is that the initial velocity is zero. The average velocity in the first second (going from zero to 10 m/s) is 5 m/s.

Second 1 = 5 m traveled.

At second 2 the particle is already moving at 10 m/s thus it's average velocity is 10 m/s.

Second 2 = 15 m traveled.

Seconds 3 and 4 are the same. So 5,15,25,35 seems right to me.

 

[dextor2003]

i dont understand any of your reasonings..at least conceptually...if the particle is accelerating constantly, then the velocity is constantly increasing, meaning that the particle is traveling more distancen each second than it did during the previous second

x=1/2at^2
say a=2, so in this case that means, x is entirely dependent on t^2

time: 1 2 3 4 5
dist.: 1 4 9 16 25

now i understand the distances here are total, and that you have to subtract to get the distances traveled during each run, so that gives you...

0-1, 1m traveled
1-2, 3m traveled
2-3, 5 traveled
3-4, 7 traveled
4-5, 9 traveled

please clarify my reasoning..

 

[fizzgig]

your reasoning looks right to me..
B) is 5,15,25,35

x=.5at^2, and we know 5 is the distance at 1s
5=.5a(1), so now we know a=10

x=.5(10)(1)=5-------->from0to1s 5m
x=.5(10)(4)=20------->from1-2s 20-5=15m
x=.5(10)(9)=45------->from2-3s 45-20=25m
x=.5(10)(16)=80------>from3-4s 80-45=35m