EK 1001 Physics #56

[angkim]

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A particle moving at 5m/s reverses its direction in 1 s to move at 5m/s in the opposite direction. If it's acceleration is constant, what distance does it travel?

1.25m
2.5m
5m
10m

Answer: B
x=v0t+1/2at^2 where a=(vfinal-vinitial)/t but there is a trick. x is displacement, not distance. to find distance, you must recognize that the particle travels half the distance in half the time. thus, you plug in 1/2 the total time, only in the first equation and then solve for x and double your answer for the total distance.


I understand that x is the displacement meaning it's xfinal-xinitial.
vfinal= -5m/s
vinitial= 5m/s

but i don't understand the explanation in terms of plugging in 1/2 the total time..because i need to recognize that particle travels half the distance in half the time? Can someone please elaborate on this? What would the equation that I would be using actually look like? I've spent like 30 minutes trying to figure out my math and it's not working... 🙁 Please help! Thank you!

 

[angkim]

OKAY after taking a dinner break, I came back to the problem and tried to figure it out.

first I found a:
v_initial=5m/s
v_final= -5m/s
t=1sec

a=(vfinal-vinitial)/time = (-5-5)/1 = -10m/s^2

I guess it is a fact that half the distance takes half the total time so the time I'd would plug into the equation in the first post would be 1sec*1/2=1/2sec
then solve for x of the equation:
x= (5m/s)(1/2sec) + (1/2)(-10m/s^2)(1/2)^2
=2.5 - 1.25
=1.25m

since x solved is half the distance traveled because I used half the total time, I need to double the x to find the total distance: 1.25m x 2 = 2.5m.

I know this problem may be an easy one for many.. but I do have trouble even with the easiest concepts in physics. i would really appreciate it if someone could correct me if I'm wrong on how i got the answer. Or even just a confirmation. Thank you so much.

 

[banner18]

sometimes i hate the way EK explains things...

here's how i did it, im not as intuitive as EK expects us to be.
since there is a change of direction i wanted to find out t when v=0.

I used v=v1+at
0=5+(-10)*t
t= 1/2 sec

then use your equation.
x=5*.5+.5*-10*(.5)^2
x=1.25 m

so the particle moves 1.25m when v=0 and t=1/2 sec, you then multiply by 2 to get the total D since the acceleration is const.

the reason they talk about half the dist. is because thats when v=0. Basically this is a projectile motion problem is disguise, its asking you to find the height a ball shot upward will reach if its given an initial v of 5 m/s. This height times 2, gives you dist. traveled.

if question was: car v1=5 m/s increases and speeds to 15 m/s in 1 sec what is the total dist? You would not need to think that it travels half the distance in have the time, you just plug and chug!

 

[npparikh90]

A particle moving at 5m/s reverses its direction in 1 s to move at 5m/s in the opposite direction. If it's acceleration is constant, what distance does it travel?

1.25m
2.5m
5m
10m

Answer: B
x=v0t+1/2at^2 where a=(vfinal-vinitial)/t but there is a trick. x is displacement, not distance. to find distance, you must recognize that the particle travels half the distance in half the time. thus, you plug in 1/2 the total time, only in the first equation and then solve for x and double your answer for the total distance.


I understand that x is the displacement meaning it's xfinal-xinitial.
vfinal= -5m/s
vinitial= 5m/s

but i don't understand the explanation in terms of plugging in 1/2 the total time..because i need to recognize that particle travels half the distance in half the time? Can someone please elaborate on this? What would the equation that I would be using actually look like? I've spent like 30 minutes trying to figure out my math and it's not working... 🙁 Please help! Thank you!

wow this question makes no sense to me and the answer. If i am reading the question corrrectly it says that a particle is moving at 5 m/s for 1 second so hence it traveled distance/displacement of 5 meters and than after one second it changes its direction so now there is acceleration before it was none and now the particle is constantly accelerating the distance it travels depends on the time it travels in reverse direction and speed none of which is listed.

P.S. i am not very good at physics so i use an intuitive approach of learning to improve my understanding of Physics but please let me know what mistake i am making in understanding this question. If I was to answer it I would pick 10 m and hence get it wrong i guess lol

 

[angkim]

sometimes i hate the way EK explains things...

here's how i did it, im not as intuitive as EK expects us to be.
since there is a change of direction i wanted to find out t when v=0.

I used v=v1+at
0=5+(-10)*t
t= 1/2 sec

then use your equation.
x=5*.5+.5*-10*(.5)^2
x=1.25 m

so the particle moves 1.25m when v=0 and t=1/2 sec, you then multiply by 2 to get the total D since the acceleration is const.

the reason they talk about half the dist. is because thats when v=0. Basically this is a projectile motion problem is disguise, its asking you to find the height a ball shot upward will reach if its given an initial v of 5 m/s. This height times 2, gives you dist. traveled.

if question was: car v1=5 m/s increases and speeds to 15 m/s in 1 sec what is the total dist? You would not need to think that it travels half the distance in have the time, you just plug and chug!

Hey Banner, I second that in regards to EK explanations.. but thanks so much for your simple explanation. Yours is much easier to understand than EK's. It is definitely projectile motion in disguise and I now get why we have to double the answer we get to get 2.5m. THANK SO MUCH SERIOUSLy!!! 😀

wow this question makes no sense to me and the answer. If i am reading the question corrrectly it says that a particle is moving at 5 m/s for 1 second so hence it traveled distance/displacement of 5 meters and than after one second it changes its direction so now there is acceleration before it was none and now the particle is constantly accelerating the distance it travels depends on the time it travels in reverse direction and speed none of which is listed.

P.S. i am not very good at physics so i use an intuitive approach of learning to improve my understanding of Physics but please let me know what mistake i am making in understanding this question. If I was to answer it I would pick 10 m and hence get it wrong i guess lol

Hi npparikh, I'm not very good at Physics either but there is acceleration since a=change in velocity/time. So i just put 5m/s as initial and -5m/s as final since it's going the opposite direction. This took 1 sec so:
a=(-5-5)/1 = -10

Now that we've found the acceleration, we can solve how banner solved it above. I'm really not sure if what I said was helpful but yeah banner explained it very well! 😳

 

[bullsfan1986]

I had trouble with this question too, but realized that there was an even easier way of solving it..

Because they only give you time as being =1 s in a positive direction, I basically just used the two equations: v=d/t and a=v/t and solved in terms of t where t=d/v and just plugged that equation in to a=v/(d/v) = v^2/d= a. And then I solved for d=25/10 = 2.5 meters. I duno if that helps.