Question

The figure shows the velocity graph of a particle moving along the x-axis (d=9.4, T=2.8). Its initial position is x0 = 3.4 m at t0 = 0 s. At t1 = 1.1 s,

Answer 1

What is the particle's velocity? What is the particle's position?

Answer 2

Are you comfortable with integration ?

Answer 3

i guess ill try

Answer 4

how would i start?

Answer 5

hello are you there?

Answer 6

v = mt

when t=T, v=2d

=> 2d = m(T)
=>m = 2d/T

hence the relation between v and t is
v = (2d/T)t

you can now find velocity of particle at t=1.1

for the position, we know
v= dx/dt
hence

dx = (2d/T)t dt

integrate both sides,
and use the fact that x=3.4 at t=0 to find the constant of integration.

Hope this helps ?

Answer 7

hold on a sec let me work it out real quick

Answer 8

Take your time.

Answer 9

i got 7.38 for the velocity

Answer 10

7.38 m/s velocity

Answer 11

Yep, seems correct.

Answer 12

im kind of confused for the position can you explain it please

Answer 13

v= dx/dt right ?

Answer 14

yes

Answer 15

so we have on that substitution,
dx/dt = (2d/T)t ?

Answer 16

yes i get that

Answer 17

=> dx = (2d/T) t dt

Answer 18

so we solve for dx right?

Answer 19

we know t=1.1 T=2.8 and d=9.4...

Answer 20

So you're not comfortable with integration!

Answer 21

i guess not im kind of rusty on integration. Im sorry

Answer 22

hmm, guess you need to learn integration before attempting this problem.

Answer 23

then can you help me with integration

Answer 24

please

Answer 25

Leme try.

2d/T = 6.71 right ?

Answer 26

correct

Answer 27

=> dx = 6.71t dt

Answer 28

ok

Answer 29

Now we integrate both sides.
Can you tell me integral of dx ?

Answer 30

would i be the anti derivative so hold on give me a sec

Answer 31

so 3.355 t^2

Answer 32

yep.
so we have
x= 3.56 t^2 + C
where C is the constant of integration, clear so far ?

Answer 33

yes its clear

Answer 34

We also know x=3.4 at t=0, use this to find C

Answer 35

ok give me a sec to solve

Answer 36

oh duh so c = 3.4

Answer 37

Yep,
so x= 3.56 t^2 + 3.4

just plug in t=1.1 to find x at that time and congrats, you're done!

Answer 38

i got 7.71m

Answer 39

And that is correct!
Bingo! ^_^

Answer 40

i plugged it in and it says its wrong

Answer 41

eh ? Try 7.7076 ?

Answer 42

it said it was wrong.

Answer 43

I don't see how that is wrong. Approximately speaking, we have done it all correct so far.

Answer 44

oh i see what we did wrong the antiderivative was 3.357 not 3.56 minor mistake.

Answer 45

but thanks alot for helping me i guess i need to brush up on calculus. Thanks alot!!

Answer 46

hmm..