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
Answer:
3. Work
Explanation:
Number 1 isn't correct because you are not using efficiency to hold books and walk across the room.
Number 2 could be correct but isn't in this situation because you use power only to hold the books but not to walk across the room.
Number 4 is not correct because you need to do work to do something.
Answer:
v = 8.63 m/s
Explanation:
Neglecting the frictional forces, the law of conservation of energy can be applied to this situation as follows:
Potential Energy Gained By Athlete = Kinetic Energy Lost By Athlete
mgh = (0.5)mv²
gh = (0.5)v²
v = √2gh
where,
v = speed that the athlete must have when he plants the pole = ?
g = acceleration due to gravity = 9.8 m/s²
h = Height to be achieved by the athlete = 3.8 m
Therefore,
v = √(2)(9.8 m/s²)(3.8 m)
<u>v = 8.63 m/s</u>