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
I can't decide between A and B, but B seems more likely to me. Even though the molecules don't look like they're moving, the area of contact is slightly more compressed.
The formula to use is the one that connects the acceleration,
the distance fallen, and the time spent falling:
Distance = 1/2 a T² .
You said 2.1 meters in 0.6 second .
2.1 m = 1/2 a (0.6 sec)²
Multiply each side by 2 : 4.2 m = a (0.6 sec)²
Divide each side by (0.6 sec)² = (4.2/0.36) m/s² = a
a = (11 and 2/3) m/s²
(about 19% more than Earth's gravity)
It's dependent on the mass. You can fimd the force needed using the formula F = ma. Where F is force, m is mass of the cart and a is the acceleration (0.9m/s^2). The heavier it is the more force you are going to need. Remember unit of force is N
Answer:
C.
Explanation:
Ultraviolet light shining on the minerals will cause them to give off visible light.
