Electric potential = work done/charge of electron = 2.18×10⁻¹⁸/1.6×10⁻¹⁹
= 13.625 V
<span>(a) -9.97 m/s
(b) x = 2.83
This is a simple problem in integral calculus. You've been given part of the 2nd derivative (acceleration), but not quite. You've been given the force instead. So let's setup a function for acceleration.
f''(x) = -8x N / 3.1 kg= -8x kg*m/s^2 / 3.1 kg = -2.580645161x m/s^2
So the acceleration of the body is now expressed as
f''(x) = -2.580645161x m/s^2
Let's calculate the anti-derivative from that.
f''(x) = -2.580645161x m/s^2
f'(x) = -1.290322581x^2 + C m/s
Now let's use the known velocity value at x = 2.0 to calculate C
f'(x) = -1.290322581x^2 + C
1
1 = -1.290322581*2^2 + C
11 = -1.290322581*4 + C
11 = -5.161290323 + C
16.161290323 = C
So the velocity function is
f'(x) = -1.290322581x^2 + 16.161290323
(a) The velocity at x = 4.5
f'(x) = -1.290322581x^2 + 16.161290323
f'(4.5) = -1.290322581*4.5^2 + 16.161290323
f'(4.5) = -1.290322581*20.25 + 16.161290323
f'(4.5) = -26.12903227 + 16.161290323
f'(4.5) = -9.967741942
So the velocity is -9.97 m/s
(b) we want a velocity of 5.8 m/s
5.8 = -1.290322581x^2 + 16.161290323
0 = -1.290322581x^2 + 10.36129032
1.290322581x^2 = 10.36129032
x^2 = 8.029999998
x = 2.833725463</span>
Answer:
1. The automobile is traveling due east and is speeding up.
2. The car is traveling due east and is is slowing down.
3. The automobile is traveling due east at a constant speed.
4. The car is traveling due west and is slowing down.
5. The automobile is traveling due west and is speeding up.
6. The automobile is traveling due west at a constant speed.
7. The automobile is accelerating due east from rest.
8. The automobile is accelerating due west from rest.
Explanation:
The key to understanding this is:
When the acceleration and initial velocity of the automobile have the same sign (positive or negative) then the automobile is speeding up. Explained further, if acceleration and the initial velocity are both positive or they are both negative the automobile is speeding up but whenever they have opposite signs (that is acceleration is positive and initial velocity is negative or vice versa) the automobile is slowing down. When the acceleration is zero the automobile is maintaining a unform motion at a constant speed (the speed is not changing with time). The + or - sign indicates the direction of travel. In this case east is + and west is -. It is my pleasure answering this question. I hope you find it helpful. Thank you.
Answer:
1. Mass
2. Height
3. Gravitational Force Field
Explanation:
The three factors that decide how much gravitational potential energy a body has are: 1) The mass of the body itself, 2) The relative height at which the body is, because gravitational force varies with height i.e distance away from earth surface. 3) and finally the strength of the gravitational field the body is in.
