Answer and Explanation:
Let:

The equation representing a simple harmonic motion, where:

As you may know the derivative of the position is the velocity and the derivative of the velocity is the acceleration. So we can get the velocity and the acceleration by deriving the position:

Also, you may know these fundamental formulas:

Now, using the previous information and the data provided by the problem, let's solve the questions:
(a)

(b)

(c)

(d)
We can extract the phase of the motion, the angular frequency and the amplitude from the equation provided by the problem:

(e)

(f)

The car is staying still. either getting petrol or stopped at a light .
Answer:
speed and time are Vf = 4.43 m/s and t = 0.45 s
Explanation:
This is a problem of free fall, we have the equations of kinematics
Vf² = Vo² + 2g x
As the object is released the initial velocity is zero, let's look at the final velocity with the equation
Vf = √( 2 g X)
Vf = √(2 9.8 1)
Vf = 4.43 m/s
This is the speed with which it reaches the ground
Having the final speed we can find the time
Vf = Vo + g t
t = Vf / g
t = 4.43 / 9.8
t = 0.45 s
This is the time of fall of the body to touch the ground
Answer:
h' = 603.08 m
Explanation:
First, we will calculate the initial velocity of the pellet on the surface of Earth by using third equation of motion:
2gh = Vf² - Vi²
where,
g = acceleration due to gravity on the surface of earth = - 9.8 m/s² (negative sign due to upward motion)
h = height of pellet = 100 m
Vf = final velocity of pellet = 0 m/s (since, pellet will momentarily stop at highest point)
Vi = Initial Velocity of Pellet = ?
Therefore,
(2)(-9.8 m/s²)(100 m) = (0 m/s)² - Vi²
Vi = √(1960 m²/s²)
Vi = 44.27 m/s
Now, we use this equation at the surface of moon with same initial velocity:
2g'h' = Vf² - Vi²
where,
g' = acceleration due to gravity on the surface of moon = 1.625 m/s²
h' = maximum height gained by pellet on moon = ?
Therefore,
2(1.625 m/s²)h' = (44.27 m/s)² - (0 m/s)²
h' = (1960 m²/s²)/(3.25 m/s²)
<u>h' = 603.08 m</u>
Answer:
s = 589.3 m
Explanation:
Let the truck and car meet at a distance = s m
The truck is moving at constant velocity = v
so s= v * t ---------- (1)
car:
Vi = 0 m/s
a = 3.9 m/s²
s = Vi* t + 1/2 a t²
s= 0 * t + 1/2 a t²
s = 1/2 a t² ----------- (2)
compare equation (1) and equation (2)
s= v * t = 1/2 a t²
⇒ v * t = 1/2 a t²
⇒ t = 2 * v/ a
⇒ t = (2 * 33.9 )/ 3.9
⇒ t = 17. 38 s
Now
from equation (1)
s= v * t
s= 33.9 * 17.38
⇒ s = 589.3 m