The position of the particle is given by:
x(t) = t³ - 12t² + 21t - 9
Differentiate x(t) with respect to t to find the velocity x'(t):
x'(t) = 3t² - 24t + 21
Differentiate x'(t) with respect to t to find the acceleration x''(t):
x''(t) = 6t - 24
Answer:
<h2>64.4 N</h2>
Explanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question
mass = 9.2 kg
acceleration = 7 m/s²
We have
force = 9.2 × 7 = 64.4
We have the final answer as
<h3>64.4 N</h3>
Hope this helps you
No. The correct one would be D .
Answer:
Part a)
![F = 135.7 N](https://tex.z-dn.net/?f=F%20%3D%20135.7%20N)
Part b)
![F = 62.5 N](https://tex.z-dn.net/?f=F%20%3D%2062.5%20N)
Explanation:
Part a)
If block is sliding up then net force must be zero and friction will be in opposite to the direction of motion of the block
![Fcos\theta = mg + F_f](https://tex.z-dn.net/?f=Fcos%5Ctheta%20%3D%20mg%20%2B%20F_f)
![Fsin\theta = F_n](https://tex.z-dn.net/?f=Fsin%5Ctheta%20%3D%20F_n)
so we have
![Fcos\theta = mg + \mu(Fsin\theta)](https://tex.z-dn.net/?f=Fcos%5Ctheta%20%3D%20mg%20%2B%20%5Cmu%28Fsin%5Ctheta%29)
![F(cos\theta - \mu sin\theta) = mg](https://tex.z-dn.net/?f=F%28cos%5Ctheta%20-%20%5Cmu%20sin%5Ctheta%29%20%3D%20mg)
![F = \frac{mg}{cos\theta - \mu sin\theta}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bmg%7D%7Bcos%5Ctheta%20-%20%5Cmu%20sin%5Ctheta%7D)
![F = \frac{55}{cos50 - 0.310(sin50)}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B55%7D%7Bcos50%20-%200.310%28sin50%29%7D)
![F = 135.7 N](https://tex.z-dn.net/?f=F%20%3D%20135.7%20N)
Part b)
If block is sliding down then net force must be zero and friction will be in opposite to the direction of motion of the block
![Fcos\theta = mg - F_f](https://tex.z-dn.net/?f=Fcos%5Ctheta%20%3D%20mg%20-%20F_f)
![Fsin\theta = F_n](https://tex.z-dn.net/?f=Fsin%5Ctheta%20%3D%20F_n)
so we have
![Fcos\theta = mg - \mu(Fsin\theta)](https://tex.z-dn.net/?f=Fcos%5Ctheta%20%3D%20mg%20-%20%5Cmu%28Fsin%5Ctheta%29)
![F(cos\theta + \mu sin\theta) = mg](https://tex.z-dn.net/?f=F%28cos%5Ctheta%20%2B%20%5Cmu%20sin%5Ctheta%29%20%3D%20mg)
![F = \frac{mg}{cos\theta + \mu sin\theta}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bmg%7D%7Bcos%5Ctheta%20%2B%20%5Cmu%20sin%5Ctheta%7D)
![F = \frac{55}{cos50 + 0.310(sin50)}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B55%7D%7Bcos50%20%2B%200.310%28sin50%29%7D)
![F = 62.5 N](https://tex.z-dn.net/?f=F%20%3D%2062.5%20N)