Mechanics Help!!! PLZ!!!

kk i got some q's on mechanics, and im useless at mechanics, or some parts of mechanics. i really need the help as i got about 3 q's to do, i'd like to say thanks in advance if u can solve them, as i've already and still am trying :mad:

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1 Two particles, X and Y are moving in the same direction on parallel horizontal tracks. At a certain point O, the particle X, travelling with a speed of 16m/s and retarding uniformaly at 6m/s, overtakes Y, which is travelling at 8m/s and accelerating uniformaly at 2m/s. Calculate:

i - the distance of Y from O when the velocities of X and Y are equal,
ii - the velocity of X when Y overtakes X

2 a - A particle is projected vertically upwards with velocity 12m/s. Calculate:

i - the greatest height reached,
ii - its speed when it is at a height of 4m

b/Two Particles A and B are 96m apart on a smooth horizontal surface. A is moving directly towards B with speed 7m/s and retardation 2m/s. B is moving directly towards A with speed with 3m/s and accelerating 4m/s. Calculate the time taken before they meet

3/When t=0 (where t denotes time in seconds) a particle A moves from a point O along a straight line with inital velocity u m/s and constant acceleration a m/s. When t=4, a particle B moves from O along the straight line with inital velocity ½u m/s and constant velocity 2a m/s.

Given that when t=16, A is ahead of B, obtain in terms of u and a an expression for the distance between the particles at that time

Given also that this distance is 12m, and that the velocity of A when t=16 is 10m/s calculate

i - the value of u and of a

Hence calculate when t=18

ii- the distance between the particles
iii- the difference between their velocities

Reply 1

misslucy

This could be very wrong as I'm not the best at Mechanics. But for the second question I got: 7.35m and 8.10ms-2

Reply 2

IsOLaTiOnIsT

OP

2

yeh i've just worked question 1 and 2 out its just question 3 i need to do, yeh ur answers are right for q2

Reply 3

generalebriety

16

IsOLaTiOnIsT

3/When t=0 (where t denotes time in seconds) a particle A moves from a point O along a straight line with inital velocity u m/s and constant acceleration a m/s. When t=4, a particle B moves from O along the straight line with inital velocity ½u m/s and constant velocity 2a m/s.

Given that when t=16, A is ahead of B, obtain in terms of u and a an expression for the distance between the particles at that time

I assume the bolded word is meant to be acceleration...

Using s = ut + 1/2 at^2, I get the distance is (10u - 16a)m.

Given also that this distance is 12m, and that the velocity of A when t=16 is 10m/s calculate

i - the value of u and of a

10u - 16a = 12.

Use v = u+at to get a similar expression for the velocity, and solve simultaneously: u = 2ms^-1, a = 1/2 ms^-2.

Hence calculate when t=18

ii- the distance between the particles
iii- the difference between their velocities

You should be able to do this now. :smile:

Reply 4

IsOLaTiOnIsT

OP

2

1)
i)

Consider X

using v=u+at
v=16+(-6)t
v=16-6t (1)

Consider Y

using v=u+at
v=8+2t (2)

equate (1) and (2)

16-6t = 8+2t
8=8t
t=1

when t=1 for Y
using s=ut+0.5at
s=8(1)+0.5(2)(1)
s=9m

ii)
For X
v=u+at
v=16+(-6)(1)
v=10 m/s

2)
a)i)
using v=u+2as
0=12+2(-10)h
0=144-20h
h=144/20
h=7.2m

ii)
using v=u+2as
v=12+2(-10)(4)
v=64
v=8m/s

Consider A
let dist travelled by A = x
using s=ut+0.5at
x=7t+0.5(-2)t
x=7t-t

Consider B
let dist. travelled be y
using s=ut+0.5t
y=3t+0.5(4)t
y=3t+2t

but x+y = 96
so 7t-t+3t+2t=96
10t+t=96
t+10t-96=0
(t+16)(t-6)=0
t=-16 or t=6
since t>0 then t=6 seconds

for 2ai and 2aii i forgot to mention when i posted that u have to take g to be 10m/s leading to a=g....just have to do q3 now :smile:

Reply 5

Christophicus

18

3/When t=0 (where t denotes time in seconds) a particle A moves from a point O along a straight line with inital velocity u m/s and constant acceleration a m/s. When t=4, a particle B moves from O along the straight line with inital velocity ½u m/s and constant velocity 2a m/s.

Given that when t=16, A is ahead of B, obtain in terms of u and a an expression for the distance between the particles at that time

Particle A
s = ut + 0.5at^2

Particle B
s = 0.5u(t-4) + 0.5(2a)(t-4)^2 = 0.5u(t-4) + a(t-4)^2

At t = 16, Sa > Sb
Therefore distance between particles
= ut+0.5at^2-0.5u(t-4)-a(t-4)^2

At t = 16, distance between particles
= 16u+0.5a(16)^2-0.5u(16-4)-a(16-4)^2
= 16u+128a-6u-144a
= 10u-16a

Given also that this distance is 12m, and that the velocity of A when t=16 is 10m/s calculate;
i - the value of u and of a

10u-16a = 12 (1)

Va = u+at
At t = 16
10 = u+16a (2)

(1)+(2)
11u = 22
u = 22/11 = 2m/s

a = (10-u)/16 = (10-2)/16 = 8/16 = 0.5m/s^2

Hence calculate when t=18
ii- the distance between the particles
iii- the difference between their velocities

At t = 18
Sa = 2(18) + 0.5(0.5)(18)^2 = 117m
Sb = 0.5(2)(18-4) + (0.5)(18-4)^2 = 112m

Therefore distance between the particles at t = 18 is 5m

At t = 18
Va = u+at = 2+0.5(18) = 11m/s
Vb = 0.5u + 2a(t-4) = 0.5(2) + 2(0.5)(18-4) = 15m/s

Therefore the difference between their velocities at t = 18 is 4m/s

Reply 6

IsOLaTiOnIsT

OP

2

cheers for the help ppl :smile:

nearly got out 3 for myself, i made a few errors though :frown:

Reply 7

generalebriety

16

Widowmaker

[some long post]

Christ, Widowmaker, have you never heard of subtle hints? :rolleyes:

Reply 8

generalebriety

16

IsOLaTiOnIsT

cheers for the help ppl :smile:

nearly got out 3 for myself, i made a few errors though :frown:

Inevitable in mechanics. Question 3 is easy actually but then when I was learning that topic I didn't think so. It's one of those subjects - you think everything's hard when you first do it, but then once you move off it and do something else it becomes easy. :confused:

Interesting subject though. :p:

Reply 9

IsOLaTiOnIsT

OP

2

challenging subject, got the exam in januray, seems far away but im still struggling, probs understand most of it near the time though

Reply 10

insparato

15

Mechanics is a challenge but as far as im concerned im keeping well away just because i need my A i dont care enough about maths to want to do it as a challenge.

Reply 11

cuddy

3

yeah mechanics is tough at first, but once you master it it feels good :P The summer m1 exam was nice as well

Mechanics Help!!! PLZ!!!

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