Answer:
A sample of 5.2 mg decays to .65 mg or to 1/8 of its original amount.
1/8 = 1/2 * 1/2 * 1/2 or 3 half-lives.
3 * 30.07 = 90 yrs for 5.2 mg to decay to .65 mg
You can get these other numbers similarly:
5.2 / .0102 = 510 requires about 9 half-lives which is 30 * 9 = 270 yrs
Answer:
Period of motion is approximately 0.5447 seconds
Explanation:
We start by calculating the constant "k" of the spring which can be derived from the fact that an object of mass 12 g produced a stretch of 3.4 cm: (we write everything in SI units)
F = k * x
0.012 kg * 9.8 m/s^2 = k 0.034 m
k = 0.012 kg * 9.8 m/s^2 / (0.034 m)
k = 3.46 N/m
now we use the formula for the period (T) of a spring of constant k with a hanging mass 'm':

which in our case becomes:

Answer:
1.52905 seconds
4.58715 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
= Coefficient of friction = 0.4
g = Acceleration due to gravity = 9.81 m/s²
a = Acceleration = 
Equation of motion

It will take 1.52905 seconds for the block to slow down

The block will travel 4.58715 m before it stops
Answer:
4 m
Explanation:
From the question given above, the following data were obtained:
Initial velocity (u) = 10 m/s
Acceleration (a) = –8m/s²
Time (t) = 2 s
Displacement (s) =?
The displacement of the object can be obtained as follow:
s = ut + ½at²
s = (10 × 2) + (½ × –8 × 2²)
s = 20 + (–4 × 4)
s = 20 + (–16)
s = 20 – 16
s = 4 m
Thus, the displacement of the object is 4 m.
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