To solve this problem we will use the kinematic equations of angular motion in relation to those of linear / tangential motion.
We will proceed to find the centripetal acceleration (From the ratio of the radius and angular velocity to the linear velocity) and the tangential acceleration to finally find the total acceleration of the body.
Our data is given as:
The angular speed
The angular acceleration
The distance
The relation between the linear velocity and angular velocity is

Where,
r = Radius
Angular velocity
At the same time we have that the centripetal acceleration is






Now the tangential acceleration is given as,

Here,
Angular acceleration
r = Radius


Finally using the properties of the vectors, we will have that the resulting component of the acceleration would be



Therefore the correct answer is C.
The elastic potential energy of the spring is 6.8 J
Explanation:
The elastic potential energy of a compressed/stretched spring is given by the equation:

where
k is the spring constant
x is the elongation of the spring
The spring constant of the spring in this problem can be found by keeping in mind the relationship between force (F) and elongation (x) (Hooke's law):

By looking at the graph and comparing it with the formula, we realize that the slope of the force-elongation graph corresponds to the spring constant. Therefore in this case,

Therefore when the spring has a elongation of
, its potential energy is

Learn more about potential energy:
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Answer:
The new planet has more gravity
Explanation:
gravity force = G m1 m2 / r^2
decresing r or increasing the planet mass will increase the force
Answer:
Wellll. I am assuming the direction of speed is in the same direction as the direction of displacement of the train. (i.e. Velocity is positive)
Acceleration is defined as the rate of change of velocity with respect to time (m^s-2)
Explanation:
The complete question in the attached figure
Let
c ------------------- > is the speed of light
v ------------------- > is the speed in medium
n ------------------- > is the refractive index of medium
we know that
c/v = n
n = (3 x 10^8)/(2.04 x 10^8) = 1.47
1.47 is the refractive index of glycerol.
therefore
the answer is (4) glycerol