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:
Horizontal distance=?m
Explanation:
Horizontal velocity,u=482ms⁻¹
Height of the cliff=17.7m
Horizontal distance,R=?
R=v×√2h/g
Answer: 6 and 8 would be side lengths because if it has a scale factor of 2 then you multiply the ones on the chart.
Explanation:Go find one
Answer:
(A). The rotational momentum of the flywheel is 12.96 kg m²/s.
(B). The rotational speed of sphere is 400 rad/s.
Explanation:
Given that,
Mass of disk = 10 kg
Radius = 9.0 cm
Rotational speed = 320 m/s
(A). We need to calculate the rotational momentum of the flywheel.
Using formula of momentum
Put the value into the formula
(B). Rotation momentum of sphere is same rotational momentum of the flywheel
We need to calculate the magnitude of the rotational speed of sphere
Using formula of rotational momentum
Put the value into the formula
Hence, (A). The rotational momentum of the flywheel is 12.96 kg m²/s.
(B). The rotational speed of sphere is 400 rad/s.
