Prelim 2016 Maths Help Thread (1 Viewer)

[Paradoxica]

I just hit a key combo and whatever Unicode Symbol I want appears.

Customisation is da best )))))

 

[eyeseeyou]

Some more motion questions:

Motion defined by v=v(x)
1.The velocity of a body is given by v=⁡〖(cos⁡(x^2)x)/(1+sinxcosx).〗find the value of t when x=π/4 if P starts from the origin
2.The velocity of a particle moving on the x-axis is given by v= (squareroot of sinx) e^(x/2), 0≤x≤pi/3, where x is the displacement of the particle from the origin
a.Show that the acceleration of the particle in terms of its displacement can be expressed by a=1/2 e^(-x) (cosx-sinx)
b.Hence find the displacement of the particle at which the maximum speed occurs
3.A particle moves in a straight line. At time t seconds its displacement is x metres from a fixed point O on the line, its acceleration is a m/s^2 and its velocity is v m/s where v is given by 32/x – x/2. The particle starts 2 metres to the right O
a.Find an expression for a in terms of x
b.Show that t=ꭍ2x/(64-x^2) dx and hence show that x^2=64-60e^(-t)
c.Sketch the graph x^2 against t and describe the limiting behaviour of the particle
Motion defined by a=a(x)
1.The acceleration of a particle in a straight line is given by x’’=-2e^(-x) where x m is the displacement from the origin . Initially the particle is at the origin with velocity 2 m/s
a.Prove that v=2e〖^(-x/2)〗
b.What happens to v as x increase without bound?
2.The acceleration of a body moving along a straight line is given by:
(d^2 x)/(dt^2 )=-24/(x^2)
Where x is the displacement from the origin after t seconds. When t=0 the body is 3 metres to the right of the origin with a velocity of 4m/s
a.Show that the velocity, v, of the body in terms of x is given by v= 4squareroot of 3/ squar root of x
b.Find an expression for t in terms of x
c.How long does it take for the body to reach a point 10m to the right of the origin?
3.A particle P moves in the straight line XOX’ so that its acceleration x’’ when its displacement from 0 is x, is given by x’’= 1/squareroot (4-x^2) + 1/(9+x^2) and hence, if P is projected from O with velocity squareroot of pi, prove that 1/2v^2= (inverse of sin) x/2+1/3tan(inverse)x/3 + pi/2. Find (in terms of pi), the speed of the particle when it is squareroot of 3 units on the
a.Positive
b.Negative side of 0
Leehuan/Integrand/David need your help

 

[eyeseeyou]

Some more motion questions:

Motion defined by v=v(x)
1.The velocity of a body is given by v=⁡〖(cos⁡(x^2)x)/(1+sinxcosx).〗find the value of t when x=π/4 if P starts from the origin
2.The velocity of a particle moving on the x-axis is given by v= (squareroot of sinx) e^(x/2), 0≤x≤pi/3, where x is the displacement of the particle from the origin
a.Show that the acceleration of the particle in terms of its displacement can be expressed by a=1/2 e^(-x) (cosx-sinx)
b.Hence find the displacement of the particle at which the maximum speed occurs
3.A particle moves in a straight line. At time t seconds its displacement is x metres from a fixed point O on the line, its acceleration is a m/s^2 and its velocity is v m/s where v is given by 32/x – x/2. The particle starts 2 metres to the right O
a.Find an expression for a in terms of x
b.Show that t=ꭍ2x/(64-x^2) dx and hence show that x^2=64-60e^(-t)
c.Sketch the graph x^2 against t and describe the limiting behaviour of the particle
Motion defined by a=a(x)
1.The acceleration of a particle in a straight line is given by x’’=-2e^(-x) where x m is the displacement from the origin . Initially the particle is at the origin with velocity 2 m/s
a.Prove that v=2e〖^(-x/2)〗
b.What happens to v as x increase without bound?
2.The acceleration of a body moving along a straight line is given by:
(d^2 x)/(dt^2 )=-24/(x^2)
Where x is the displacement from the origin after t seconds. When t=0 the body is 3 metres to the right of the origin with a velocity of 4m/s
a.Show that the velocity, v, of the body in terms of x is given by v= 4squareroot of 3/ squar root of x
b.Find an expression for t in terms of x
c.How long does it take for the body to reach a point 10m to the right of the origin?
3.A particle P moves in the straight line XOX’ so that its acceleration x’’ when its displacement from 0 is x, is given by x’’= 1/squareroot (4-x^2) + 1/(9+x^2) and hence, if P is projected from O with velocity squareroot of pi, prove that 1/2v^2= (inverse of sin) x/2+1/3tan(inverse)x/3 + pi/2. Find (in terms of pi), the speed of the particle when it is squareroot of 3 units on the
a.Positive
b.Negative side of 0
Leehuan/Integrand/David need your help

Ans are (for v=v(x))
1. x=3
2. max occurs when a=0, e^x/2(cosx-sinx)=0...tanx=1,...x=pi/4
3. a. x''=-1024/(x^3) = pi/4
b. the particle slows down to x=8

a=a(x)
1.a. v=2e^(-x/2)
b. v approaches 0 (as in v arrow 0)
3. a. 4squrroot of pi/3
b. Squreroot of 2pi/3

 

[Nailgun]

I just hit a key combo and whatever Unicode Symbol I want appears.

Customisation is da best )))))

autohotkey?

 

[davidgoes4wce]

Some more motion questions:

Motion defined by v=v(x)
1.The velocity of a body is given by v=⁡〖(cos⁡(x^2)x)/(1+sinxcosx).〗find the value of t when x=π/4 if P starts from the origin

 

[eyeseeyou]

cos squared x

 

[eyeseeyou]

Integrand, leehuan, where are you guys when I need help?

 

[leehuan]

Can you please not just throw like 10 questions at once... and maybe at most THREE PARTS at a time

I have to attend my uni classes as well you know... looking at all of that I'm just like ok I have a bit of free time now which question do I even answer

 

[Shuuya]

Ans are (for v=v(x))
1. x=3
2. max occurs when a=0, e^x/2(cosx-sinx)=0...tanx=1,...x=pi/4
3. a. x''=-1024/(x^3) = pi/4
b. the particle slows down to x=8

a=a(x)
1.a. v=2e^(-x/2)
b. v approaches 0 (as in v arrow 0)
3. a. 4squrroot of pi/3
b. Squreroot of 2pi/3

The question says to find the value of t and your answer has a value for x?

 

[InteGrand]

Some more motion questions:

Motion defined by v=v(x)
1.The velocity of a body is given by v=⁡〖(cos⁡(x^2)x)/(1+sinxcosx).〗find the value of t when x=π/4 if P starts from the origin
2.The velocity of a particle moving on the x-axis is given by v= (squareroot of sinx) e^(x/2), 0≤x≤pi/3, where x is the displacement of the particle from the origin
a.Show that the acceleration of the particle in terms of its displacement can be expressed by a=1/2 e^(-x) (cosx-sinx)
b.Hence find the displacement of the particle at which the maximum speed occurs
3.A particle moves in a straight line. At time t seconds its displacement is x metres from a fixed point O on the line, its acceleration is a m/s^2 and its velocity is v m/s where v is given by 32/x – x/2. The particle starts 2 metres to the right O
a.Find an expression for a in terms of x
b.Show that t=ꭍ2x/(64-x^2) dx and hence show that x^2=64-60e^(-t)
c.Sketch the graph x^2 against t and describe the limiting behaviour of the particle
Motion defined by a=a(x)
1.The acceleration of a particle in a straight line is given by x’’=-2e^(-x) where x m is the displacement from the origin . Initially the particle is at the origin with velocity 2 m/s
a.Prove that v=2e〖^(-x/2)〗
b.What happens to v as x increase without bound?
2.The acceleration of a body moving along a straight line is given by:
(d^2 x)/(dt^2 )=-24/(x^2)
Where x is the displacement from the origin after t seconds. When t=0 the body is 3 metres to the right of the origin with a velocity of 4m/s
a.Show that the velocity, v, of the body in terms of x is given by v= 4squareroot of 3/ squar root of x
b.Find an expression for t in terms of x
c.How long does it take for the body to reach a point 10m to the right of the origin?
3.A particle P moves in the straight line XOX’ so that its acceleration x’’ when its displacement from 0 is x, is given by x’’= 1/squareroot (4-x^2) + 1/(9+x^2) and hence, if P is projected from O with velocity squareroot of pi, prove that 1/2v^2= (inverse of sin) x/2+1/3tan(inverse)x/3 + pi/2. Find (in terms of pi), the speed of the particle when it is squareroot of 3 units on the
a.Positive
b.Negative side of 0
Leehuan/Integrand/David need your help

How much progress have you made on any of those questions yourself?

 

[eyeseeyou]

How much progress have you made on any of those questions yourself?

not much...I'm trying to self learn the topic and its quite hard lol

 

[eyeseeyou]

Can you please not just throw like 10 questions at once... and maybe at most THREE PARTS at a time

I have to attend my uni classes as well you know... looking at all of that I'm just like ok I have a bit of free time now which question do I even answer

Okay leehuan soz

Next time I'll do like 5 questions at once split up into different sections of the week

 

[eyeseeyou]

The question says to find the value of t and your answer has a value for x?

I think i looked at the wrong answers. Could you help me Shuuya, it'd be greatly appreciated

Thanks

 

[InteGrand]

not much...I'm trying to self learn the topic and its quite hard lol

Have you asked your teacher (or tutor if you go tutoring) for help with them?

 

[Shuuya]

 

[eyeseeyou]

Thanks m8

Greatly appreciated

 

[leehuan]

Oi Nailgun how is this handwriting not feminine.

 

[eyeseeyou]

Have you asked your teacher (or tutor if you go tutoring) for help with them?

it's gonna be too many q's for them and they'll get pissed ( I think)

 

[leehuan]

it's gonna be too many q's for them and they'll get pissed ( I think)

Here's the thing it's also too many questions for us.

What year are you in again? Cause for some reason I had the belief you were in Yr 11...

 

[eyeseeyou]

Oi Nailgun how is this handwriting not feminine.

stop harrassing Shuuya