Answer:
a) The magnitude of the force is 968 N
b) For a constant speed of 30 m/s, the magnitude of the force is 1,037 N
Explanation:
<em>NOTE: The question b) will be changed in other to give a meaningful answer, because it is the same speed as the original (the gallons would be 1.9, as in the original).</em>
Information given:
d = 106 km = 106,000 m
v1 = 28 m/s
G = 1.9 gal
η = 0.3
Eff = 1.2 x 10^8 J/gal
a) We can express the energy used as the work done. This work has the following expression:

Then, we can derive the magnitude of the force as:

b) We will calculate the force for a speed of 30 m/s.
If the force is proportional to the speed, we have:

Answer:

Explanation:
From the question we are told that:
Radius 
Charge Density 
Distance
Generally the equation for electric field is mathematically given by



For the first question, you got them right, for the two you left blank, initial(beginning) velocity: 2 m/s the final velocity is: 12 m/s
Answer:
1.02 m/s²
Explanation:
The following data were obtained from the question:
Initial velocity (u) = 0 m/s
Final velocity (v) = 6.6 m/s
Time (t) = 6.5 s
Acceleration (a) =.?
Acceleration can simply be defined as the change of velocity with time. Mathematically, it can be expressed as:
a = (v – u) / t
Where:
a is the acceleration.
v is the final velocity.
u is the initial velocity.
t is the time.
With the above formula, we can obtain the acceleration of the car as follow:
Initial velocity (u) = 0 m/s
Final velocity (v) = 6.6 m/s
Time (t) = 6.5 s
Acceleration (a) =.?
a = (v – u) / t
a = (6.6 – 0) / 6.5
a = 6.6 / 6.5
a = 1.02 m/s²
Therefore, the acceleration of the car is 1.02 m/s²
Answer:
option (a) 0.61 s
Explanation:
Given;
Time taken by the ball to reach the ground = 0.50 s
Let us first calculate the distance through which the ball falls on the ground
from the Newton's equation of motion, we have

where,
s is the distance
a is the acceleration
t is the time
here it is the case of free fall
thus, a = g = acceleration due to gravity
u = initial speed of the ball = 0
on substituting the values, we get

or
s = 1.225 m
Now,
when the elevator is moving up with speed of 1.0 m/s
the initial speed of the ball = -1.0 m/s (as the elevator is moving in upward direction)
thus , we have

or

or
4.9t^2 - t - 1.225 = 0
or
t = 0.612 s
hence, the correct answer is option (a) 0.61 s