Displacement depends upon the path taken as it is a vector.
From your problem above we would have a total displacement of;
Defining +x direction as east and -x direction as west
6east-3west+1east+6east-7west
6-3+1+6-7=3 blocks east or + x-direction
So even though they walked a total of 17 blocks it ends up only being 3 blocks total in +xdirection that was travelled by displacement.
Any questions please ask.
K.E = 1/2*m*v^2 = 1/2(500)(3)^2 = 2250 J
m*g*h = 500(9.8)(30) = 147000 J
2250 + 147000 = 149250
Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
The answer to this would inFact be A
