Answer: 8.1 x 10^24
Explanation:
I(t) = (0.6 A) e^(-t/6 hr)
I'll leave out units for neatness: I(t) = 0.6e^(-t/6)
If t is in seconds then since 1hr = 3600s: I(t) = 0.6e^(-t/(6 x 3600) ).
For neatness let k = 1/(6x3600) = 4.63x10^-5, then:
I(t) = 0.6e^(-kt)
Providing t is in seconds, total charge Q in coulombs is
Q= ∫ I(t).dt evaluated from t=0 to t=∞.
Q = ∫(0.6e^(-kt)
= (0.6/-k)e^(-kt) evaluated from t=0 to t=∞.
= -(0.6/k)[e^-∞ - e^-0]
= -0.6/k[0 - 1]
= 0.6/k
= 0.6/(4.63x10^-5)
= 12958 C
Since the magnitude of the charge on an electron = 1.6x10⁻¹⁹ C, the number of electrons is 12958/(1.6x10^-19) = 8.1x10^24 to two significant figures.
Answer:
1.52s
Explanation:
Given parameters:
Acceleration = 63m/s²
Final velocity = 96m/s
Unknown:
Time taken = ?
Solution:
To solve this problem, we use one of the kinematics equation:
v = u + at
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time taken
So;
96 = 0 + 63t
t = 1.52s
Answer:
Explanation:
Check the attachment.
By the definition of the simple harmonic motion,
The motion of a particle whose acceleration is
1. Always directed towards the center of the motion.
2. Proportional to the distance from center of the motion.
We get, a ∝ -x
where
a = acceleration
x = distance of the particle from center of the motion
- sign says acceleration is in opposite direction of motion
Check the other attachment for proof of a = -ω²x (or a = -ω²y)
x and y are both use to denote distance from center of the motion
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Answer:
b 1.39 m/s²
Explanation:
Given the following data;
Time = 12 seconds
Distance, S = 100 m
Since it's starting from rest, the initial velocity is equal to 0m/s.
To find the acceleration, we would use the second equation of motion;
Where;
S represents the displacement or height measured in meters.
u represents the initial velocity measured in meters per seconds.
t represents the time measured in seconds.
a represents acceleration measured in meters per seconds square.
Substituting into the equation, we have;
100 = 0(12) + ½*a*12²
100 = 0 + 72
100 = 72a
Acceleration, a = 100/72
Acceleration, a = 1.389 ≈ 1.39 m/s²
