Explanation:
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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
==>
As it is given that the air bag deploy in time
total distance moved by the front face of the bag
Now we will use kinematics to find the acceleration
now as we know that
so we have
so the acceleration is 400g for the front surface of balloon
C.) The measuring unit of "Electrical Power" is "Watt"
Hope this helps!
The formula for average speed is S=D/T
1. S=72m/37s
Divide
S= 1.94
Kira's average speed is 1.94m/s.
2. S=7.5km / 1.5h
S=5
Your average speed is 5km/h
3. S=1260km/3.5h
S=360
The airplanes average speed is 360km/h
