Answer:
v_max = (1/6)e^-1 a
Explanation:
You have the following equation for the instantaneous speed of a particle:
(1)
To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:
![\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%28t%29%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bate%5E%7B-6t%7D%5D%3Da%5B%281%29e%5E%7B-6t%7D%2Bt%28e%5E%7B-6t%7D%28-6%29%29%5D)
(2)
where you have use the derivative of a product.
Next, you equal the expression (2) to zero in order to calculate t:
![a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}](https://tex.z-dn.net/?f=a%5B%281%29e%5E%7B-6t%7D-6te%5E%7B-6t%7D%5D%3D0%5C%5C%5C%5C1-6t%3D0%5C%5C%5C%5Ct%3D%5Cfrac%7B1%7D%7B6%7D)
For t = 1/6 you obtain the maximum speed.
Then, you replace that value of t in the expression (1):
hence, the maximum speed is v_max = ((1/6)e^-1)a
Answer:
Explanation:
Given that
Mass of bowling ball M1=7.2kg
The radius of bowling ball r1=0.11m
Mass of billiard ball M2=0.38kg
The radius of the Billiard ball r2=0.028m
Gravitational constant
G=6.67×10^-11Nm²/kg²
The magnitude of their distance apart is given as
r=r1+r2
r=0.028+0.11
r=0.138m
Then, gravitational force is given as
F=GM1M2/r²
F=6.67×10^-11×7.2×0.38/0.138²
F=9.58×10^-9N
The force of attraction between the two balls is
F=9.58×10^-9N
The time for the car to drive directly south is determined as 7.15 s.
<h3>Time for the car to drive directly west</h3>
The time for the car to drive directly south is determined by applying the concept of slope.
slope = Δy/Δx
a = Δv/Δt
Δt = Δv/a
Δt = (26.8)/(3.75)
Δt = 7.15 s
Thus, the time for the car to drive directly south is determined as 7.15 s.
Learn more about acceleration here: brainly.com/question/605631
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That's a molecule of Butane.
It's made out of 4 Carbon atoms and 10 Hydrogen atoms.
Energy at motion is: Kinetic energy
