What are some challenging physics questions on motion and acceleration?

[gakusei_98]

dear all,
I started to study the physics during this summer holiday, I bought some books and I could not slove below questions which found in the books, I do not know to use which equation is correct...
does anyone experts can help me ?

-----(v=s/t; s=1/2(u+v)t; v=u+at; s=ut+1/2at^2; v^2=u^2+2as)
1. A car starts from rest with a uniform acceleratin of 0.6ms^-2. A second car B starts from the some point, 4 seconds later and follows the same path with an acceleration of 0.9ms^-2. How far will the cars have traveled when B passes A ?
* I think ...u=0m/s a=0.6ms^-2; a=0.9ms^-2 t=4s g=-9.81m/s^2

-----(v=u-gt; s=ut-1/2gt^2; v^2=u^2-2gs)
2. A stone is falling freely, has an instantaneous velocity of 25m/s^-1, having started from rest. Calculate (a) how long it has been falling? (b) how far it has fallen? (c)its velocity after falling for a further 3.5 secnds? (d) the distance it has convered during these 3.5 seconds?
* I think...u=0m/s v=25m/s^-1 t=3.5s g=-9.81m/s^2

3. A tower is 100m high. One body is dropped from the top of the tower, and at the same instant another body is projected vertically upwards from the bottom, and they meet half-way up. Find (a) the initial velocity of the projected body? (b) its velocity when it neets the descending body?
* I think...d or h=100m; d1 or h1=100m/2 g=-9.81m/s^2

4. A rocket leaves its pad vertically with an acceleration of 7.5m/s^-2 which remains constant until the fuel is exhausted after 8 seconds. It then continues to travel freely in the vertical direction. Find (a) the total time taken for the rocket to reach its highest? and (b) the altitude achived?
* I think...u=7.5m/s^-2 t=8 seconds g=-9.81m/s^-2

 

[Nathanael]

1. A car starts from rest with a uniform acceleratin of 0.6ms^-2. A second car B starts from the some point, 4 seconds later and follows the same path with an acceleration of 0.9ms^-2. How far will the cars have traveled when B passes A ?
* I think ...u=0m/s a=0.6ms^-2; a=0.9ms^-2 t=4s g=-9.81m/s^2

Try writing an equation for each of the cars' distance (from the starting point) as a function of time.

Remember, the second car is not moving until t=4seconds

2. A stone is falling freely, has an instantaneous velocity of 25m/s^-1, having started from rest. Calculate (a) how long it has been falling? (b) how far it has fallen? (c)its velocity after falling for a further 3.5 secnds? (d) the distance it has convered during these 3.5 seconds?
* I think...u=0m/s v=25m/s^-1 t=3.5s g=-9.81m/s^2

Have you tried any part of this problem? Are you stuck on part (a)?

3. A tower is 100m high. One body is dropped from the top of the tower, and at the same instant another body is projected vertically upwards from the bottom, and they meet half-way up. Find (a) the initial velocity of the projected body? (b) its velocity when it neets the descending body?
* I think...d or h=100m; d1 or h1=100m/2 g=-9.81m/s^2

Try writing an equation for each of the bodies' height as a function of time (use "v" in place of the unknown velocity)

Remember, one of the bodies starts out at a height of 100m

4. A rocket leaves its pad vertically with an acceleration of 7.5m/s^-2 which remains constant until the fuel is exhausted after 8 seconds. It then continues to travel freely in the vertical direction. Find (a) the total time taken for the rocket to reach its highest? and (b) the altitude achived?
* I think...u=7.5m/s^-2 t=8 seconds g=-9.81m/s^-2

Have you tried this problem? It will be easier to help you if you show your attempt.

 

[gakusei_98]

Try writing an equation for each of the cars' distance (from the starting point) as a function of time.

Remember, the second car is not moving until t=4seconds

I tried to use this to found out the A Car but stuck in B Car and the do not know how to slove the second question...

s=ut+1/2at2
s=0*(t)+1/2(0.6)*(4)2
s=0(0)+1/2*(0.6)*(16)
s=0+1/2*(9.6)
s=0+4.8
s=4.8m (A Car)


Have you tried any part of this problem? Are you stuck on part (a)?

I tried slove as my understanding but not sure they are correct or not...
a) Calculate how long it has been falling
v=u-gt
-25=0-9.81*(t)
-25=-9.81*(t)
-25/0.981=t
-15.19s=t
b) How far it has fallen (I am not sure which formula is correct)
h=1/2gt2
h=1/2*(9.81)2
h=1/2*(96.2361)
h=-48.11m
s=ut-1/2gt^2
s=0t-1/2*(-9.81)*(-15.19)
s=0-1/2*149.01
s=-74.505m
c) Its velocity after falling for a further 3.5 seconds
v=g*t
v=(-9.81)*3.5
v=-34.33m/s2

d) The distance it has covered during these 3.5 seconds
If use this equation: s=v*t
s=-34.33*3.5
s=-120.15m
If use this equation: s=ut-1/2(g)(t)^2
s=0t-1/2(9.81)(12.25)
s=t-1/2*(120.17)
s=60.08m


Try writing an equation for each of the bodies' height as a function of time (use "v" in place of the unknown velocity)

Remember, one of the bodies starts out at a height of 100m

I tried but do not know my understanding is correct or not... and no idea in question (b)
a) Find the initial velocity of the projected body
u=9.81m/s2 s1 or h1=50m (half) s2 or h2=100m (full height)
s=ut+1/2gt2
100m=(u)*(t)+1/2*(9.81)* t2
100=ut+48.11*t2
t^2-t=48.11-100
v=u-gt
-100m=u-(9.81)*(t2)
-100=u-9.81t^2
-100+9.81=ut^2
90.19m/s=u



Have you tried this problem? It will be easier to help you if you show your attempt.

I have no idea about slove this question...
a) Find the total time taken for the rocket to reach its highest point
b) The altitude achieved.

 

[Nathanael]

I have no idea about slove this question...
a) Find the total time taken for the rocket to reach its highest point
b) The altitude achieved.

The rocket accelerates for 8 seconds at a rate of 7.5 m/s per second. What will be the final velocity after that acceleration?

Then after the first 8 seconds, it stops accelerating upwards and now is accelerating downwards at 9.8 m/s^2 (from gravity) so how long will it take for it to reach it's highest point?


P.S. If you can, it will really help me to help you if you can be more specific about what parts you don't understand

 

[gakusei_98]

The rocket accelerates for 8 seconds at a rate of 7.5 m/s per second. What will be the final velocity after that acceleration?

>about the final velocity...as my understanding is if use u=0m/s and v=7.5m/s then u=9.81m/s^2 t=8s...I think if I use v=u-gt then we already have a;u;v;t therefore I do not know how to find out the final velocity...

Then after the first 8 seconds, it stops accelerating upwards and now is accelerating downwards at 9.8 m/s^2 (from gravity) so how long will it take for it to reach it's highest point?
> as my poor physics understanding...there is no any height or distance information, I do not know how to calculate...


P.S. If you can, it will really help me to help you if you can be more specific about what parts you don't understand

Thank you very much your quick response !

 

[Nathanael]

about the final velocity...as my understanding is if use u=0m/s and v=7.5m/s then u=9.81m/s^2 t=8s...I think if I use v=u-gt then we already have a;u;v;t therefore I do not know how to find out the final velocity...

v does not equal 7.5m/s

The acceleration is what is 7.5 m/[itex]s^2[/itex]


You haven't learned that acceleration * time = (change in) velocity?

 

[Nathanael]

Sorry, I didn't notice at first that you replied to my other responses.

s=ut+1/2at2
s=0*(t)+1/2(0.6)*(4)2
s=0(0)+1/2*(0.6)*(16)
s=0+1/2*(9.6)
s=0+4.8
s=4.8m (A Car)

That is the distance that car A traveled when car B first starts moving. The car will be moving at 0.6*4=2.4 m/s right? So the equation for the car A's distance will be:
[itex]d_A=4.8+2.4t+\frac{1}{2}0.6t^2[/itex]

Now all you need to do is write an equation for [itex]d_B[/itex] as a function of time, and then solve for "t" in the equation [itex]d_A=d_B[/itex]

 

[gakusei_98]

v does not equal 7.5m/s

The acceleration is what is 7.5 m/[itex]s^2[/itex]


You haven't learned that acceleration * time = (change in) velocity?

dear sir... i am shame to tell that i have not study physics in before...i just started to study by myself... very appreciated your knidly understanding my special situation...

 

[Nathanael]

I tried slove as my understanding but not sure they are correct or not...
a) Calculate how long it has been falling
v=u-gt

The equation you want to use is v=u+at where u is the initial velocity (which is zero in this case) and a is the acceleration (in this case it is 9.8)

a) Find the initial velocity of the projected body

This one is a little tricky. What you're going to want to do is find the time that it takes for the top body to fall halfway down the building. Then you're going to need to use that time to find the initial speed of the first body (the reason is that they need to both be halfway at the same time)

So if we call the time it takes to fall halfway down the building "T" then we have:
[itex]50m=vT-\frac{1}{2}9.8T^2[/itex]

 

[Nathanael]

dear sir... i am shame to tell that i have not study physics in before...i just started to study by myself... very appreciated your knidly understanding my special situation...

Then, these problems will certainly be difficult to solve. If you can't solve them from the advice I have given so far, then I would suggest writing these problems down somewhere and saving them for later while you learn more physics.

And while you're learning physics, try to understand exactly what the formulas mean
(it will be very hard to solve problems like these if you are using formulas that you don't fully understand)

I could try to walk you through these problems but I don't think you're going to completely understand why I did it the way that I did, unless you have a stronger physics foundation.

But do not throw these problems away! Save them for later! They are excellent practice to give you a strong understanding!
P.S.
Don't be ashamed! It's absolutely excellent that you're studying physics on your own!

 

[gakusei_98]

Then, these problems will certainly be difficult to solve. If you can't solve them from the advice I have given so far, then I would suggest writing these problems down somewhere and saving them for later while you learn more physics.

And while you're learning physics, try to understand exactly what the formulas mean
(it will be very hard to solve problems like these if you are using formulas that you don't fully understand)

I could try to walk you through these problems but I don't think you're going to completely understand why I did it the way that I did, unless you have a stronger physics foundation.

But do not throw these problems away! Save them for later! They are excellent practice to give you a strong understanding!



P.S.
Don't be ashamed! It's absolutely excellent that you're studying physics on your own!

dear sir, i am very appreciated your kindly understanding and explanation as much as you could to me...you are right...to slove the problems i have is too easy for all of your experts. i will study your explanation carefully and try my best to understanding them...by the way, could you teach me anymore website for the physics beginners just like me...as you mentioned if i could not 100% understanding the physics foundation, i will not understanding physics in the future...

 

[Nathanael]

dear sir, i am very appreciated your kindly understanding and explanation as much as you could to me...you are right...to slove the problems i have is too easy for all of your experts. i will study your explanation carefully and try my best to understanding them...by the way, could you teach me anymore website for the physics beginners just like me...as you mentioned if i could not 100% understanding the physics foundation, i will not understanding physics in the future...

I don't really know of any websites. There is only one I know of (I am not a fan of them, but it's a good start) and that is khanacademy.

The first few sections should be good a good start.

 

[gakusei_98]

I don't really know of any websites. There is only one I know of (I am not a fan of them, but it's a good start) and that is khanacademy.

The first few sections should be good a good start.

thank you very much with appreciated ! i will visit there first.
again, many many thanks your great help and value information, wish i can understanding Physics like you and other experts...

 

[berkeman]

Thread is closed. @gakusei_98 -- check your PMs. You *must* show your work before we can offer tutorial help. Please also only post one question per thread. Post a question using the Homework Help template showing your initial work. Then after you are able to work through it to a solution, you may start another thread with your 2nd question, and so on.