Answer:
A) It takes the truck 8 s to catch the motorcycle.
B) The motorcycle has traveled 160 m in that time.
C) The velocity of the truck is 40 m/s at that time.
Explanation:
The equations of the position and velocity of an object moving in a straight line are as follows:
x = x0 +v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
v = velocity at time t
(A) When the the truck catches the motorcycle, both have the same position. Notice that the motorcycle moves at constant speed so that a = 0:
x truck = x motorcycle
x0 +v0 · t + 1/2 · a · t² = x0 + v · t
Placing the origin of the frame of reference at the point where the truck starts, both have an initial position of 0. The initial velocity of the truck is 0. Then:
1/2 · a · t² = v · t
solving for t:
t = 2 v/a
t = 2 · 20 m/s/ 5 m/s²
t = 8 s
It takes the truck 8 s to catch the motorcycle.
(B) Using the equation of the position of the motorcycle, we can calculate the traveled distance in 8 s.
x = v · t
x = 20 m/s · 8 s
x = 160 m
(C) Now, we use the velocity equation at time 8 s.
v = v0 + a · t
v = 0 m/s + 5 m/s² · 8 s
v = 40 m/s
This graph represents the relationship between v and t. It is shown that when t increases, v increases as well. So, these two values have direct proportional relationship.
Answer:
x ’= 1,735 m, measured from the far left
Explanation:
For the system to be in equilibrium, the law of rotational equilibrium must be fulfilled.
Let's fix a reference system located at the point of rotation and that the anticlockwise rotations have been positive
They tell us that we have a mass (m1) on the left side and another mass (M2) on the right side,
the mass that is at the left end x = 1.2 m measured from the pivot point, the mass of the right side is at a distance x and the weight of the body that is located at the geometric center of the bar
x_{cm} = 1.2 -1
x_ {cm} = 0.2 m
Σ τ = 0
w₁ 1.2 + mg 0.2 - W₂ x = 0
x =
x =
let's calculate
x = 2.9 1.2 + 4 0.2 / 8
x = 0.535 m
measured from the pivot point
measured from the far left is
x’= 1,2 + x
x'= 1.2 + 0.535
x ’= 1,735 m
Answer: Terminal velocity is achieved, therefore, when the speed of a moving object is no longer increasing or decreasing; the object's acceleration (or deceleration) is zero.
Explanation:.