Motion (1 Viewer)

[school4nerds]

Hey,

i'm having a lot of trouble with motion (using functions of displacement etc) does anyone know how i can solve this? yeah and i can do the extremely easy beginning like 1st question in cambridge but thats about it.

e.g. for Q11 Exercise 3E the question is:

11) A plane lands on a runway at 100m/s. It then brakes with a constant deceleration until it stops 2km down the runway.
a) Explain why the equation of motion is (2nd derivative) of x = -k, for some positive constant k. By integrating with respect to x, find k, and find v^2 as a function of x.

so i know at the beginning you make the 2nd derivative of x equal to d/dx (1/2 x v^2) but i cant integrate the other side because i dont know what its supposed to be or theres no x?

also, how do i integrate e to the power of negative x?

 

[fortune_cookie]

d/dx(v^2/2) = -k

-k is a constant

v^2 / 2 = -kx +C

v^2 = -2kx +D

when x=0, v=100 [ From the first sentence]

100^2 = 0 +D

D=10000

v^2 = -2kx +10000

When x=2000m, v=0 [ It stops 2km down runway]

0 = -4000k+10000

k = 2.5

v^2 = -5x +10000

 

[school4nerds]

d/dx(v^2/2) = -k

-k is a constant

v^2 / 2 = -kx +C

v^2 = -2kx +D

when x=0, v=100 [ From the first sentence]

100^2 = 0 +D

D=10000

v^2 = -2kx +10000

When x=2000m, v=0 [ It stops 2km down runway]

0 = -4000k+10000

k = 2.5

v^2 = -5x +10000

thanks!

 

[RealiseNothing]