Answer:
(a) 8.362 rad/sec
(b) 6.815 m/sec
(c) 9.446 
(d) 396.22 revolution
Explanation:
We have given that diameter d = 1.63 m
So radius 
Angular speed N = 79.9 rev/min
(a) We know that angular speed in radian per sec

(b) We know that linear speed is given by

(c) We have given final angular velocity 
And 
Time t = 63 sec
Angular acceleration is given by 
(d) Change in angle is given by

The new speed of car is 10.9 m/s
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According to the principle of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.
Mass of the railroad car, m₁ = 7950 kg
Mass of the load, m₂ = 2950 kg
It can be assumed as the speed of the car, u₁ = 15 m/s
Initially, it is at rest, u₂ = 0
Let v is the speed of the car. It can be calculated using the conservation of momentum as :




Therefore, the new speed of care is 10.9 m/s
Learn more about momentum here:
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Answer: The correct option is Option b.
Explanation:
Power is defined as the rate of work done by an object.
Mathematically,
.....(1)
And work done is the product of force exerted on the object times the displacement covered by that object.
Mathematically,

Putting this value in above equation, we get:

where,
P = power = ?W
F = Force exerted = 10N
s = Displacement = 400cm = 4m (Conversion factor: 1m = 100 cm)
t = Time taken = 8s
Putting values in above equation, we get

Hence, the correct option is Option b.
Answer:
20.60 kV
Explanation:
Capacitance of parallel plates without dielectric between them is:

with d the distance between the plates, A the area of the plates and ε₀ the constant
, so :

But the dielectric constant is defined as:

With C the effective capacitance (with the dielectric) and Co the original capacitance (without the dielectric). So, the new capacitance is:

But capacitance is related with voltage by:

with Q the charge and V the voltage, using the new capacitance and solving for V:


We can solve for the acceleration by using a kinematic equation. First we should identify what we know so we can choose the correct equation.
We are given an original velocity of 24 m/s, a final velocity of 0 m/s, and a time of 6 s. We and looking for acceleration (a) in m/s^2.
The following equation has everything we need:

So plug in the known values and solve for a:
0 = 24 + 6a
-24 = 6a
a = -4 m/s^2