A radioactive substance decays according to the formula w = 20e¡kt grams where t is the time in hours. a find k given that after
1 answer:
You might be interested in
Answer:
i) The period of the particle is 0.3 seconds
ii) The angular velocity is approximately 20.94 rad/s
iii) The linear velocity is approximately 1.047 m/s
iv) The centripetal acceleration is approximately 6.98 m/s²
Explanation:
The given parameters are;
The number of revolution of the particle, n = 800 revolution
The time it takes the particle to make 800 revolutions = 4 minutes
The dimension of the circle = 5 cm = 0.05 m
Given that the dimension of the circle is the radius of the circle, we have;
i) The period of the particle, T = The time to complete one revolution
T = 1/(The number of revolutions per second)
∴ T = 1/(800 rev/(4 min × 60 s/min)) = 3/10 s
The period, T = 3/10 seconds = 0.3 seconds
ii) The angular velocity, ω = Angle covered/(Time)
800 revolutions in 4 minutes = Angle of (800 × 2·π) in 4 minutes
∴ ω = (800 × 2·π)/(4 × 60) = 20·π/3
The angular velocity, ω = 20·π/3 rad/s ≈ 20.94 rad/s
iii) The linear velocity, v = r × ω
∴ The linear velocity, v = 0.05 m × 20·π/3 rad/s = π/3 m/s ≈ 1.047 m/s
iv) The centripetal acceleration, = v²/r
∴ The centripetal acceleration, = (π/3)²/(0.05) = 20·π/9
The centripetal acceleration, = 20·π/9 m/s² ≈ 6.98 m/s²
Answer:
Distance: 21 yd, displacement: 15 yd, gain in the play: 12 yd
Explanation:
The distance travelled by Sam is just the sum of the length of each part of Sam's motion, regardless of the direction. Initially, Sam run from the 3 yd line to the 15 yd line, so (15-3)=12 yd. Then, he run also 9 yd to the right. Therefore, the total distance is
d = 12 + 9 = 21 yd
The displacement instead is a vector connecting the starting point with the final point of the motion. Sam run first 12 yd straight ahead and then 9 yd to the right; these two motions are perpendicular to each other, so we can find the displacement simply by using Pythagorean's theorem:
Finally, the yards gained by Sam in the play are simply given by the distance covered along the forward-backward direction only. Since Sam only run from the 3 yd line to the 15 yd line along this direction, then the gain in this play was
d = 15 - 3 = 12 yd
Answer:
the velocity of the water flow is 7.92 m/s
Explanation:
The computation of the velocity of the water flow is as follows
Here we use the Bernouli equation
As we know that
= 7.92 m/s
Hence, the velocity of the water flow is 7.92 m/s
We simply applied the above formula so that the correct value could come
And, the same is to be considered