Acceleration
Problem:
A rock is thrown upwards with an initial velocity of 24.5 m/s.
What is the rocks displacement after 1.00s? What maximum height will the rock reach before starting to fall downward?
What is the rocks displacement after 1.00s? What maximum height will the rock reach before starting to fall downward?
Graphs* and explanations:
*click on graph to enlarge it
Yt Graph:
![Picture](/uploads/1/8/5/6/18566514/132143364.png)
This shows the initial movement of the rock and the rock's position as it before coming back down. The rock proceeded to go upwards them pause at it's maximum height.
VT graph:
![Picture](/uploads/1/8/5/6/18566514/833603621.png)
This shows the consistent decrease of the rock until it reaches it's maximum height. The rocks velocity began at 24.5 m/s and decreased until it reached zero.
At graph:
![Picture](/uploads/1/8/5/6/18566514/923461378.png)
This shows the constant negative acceleration of the rock as it travels upwards toward it's maximum height.
Motion map:
![Picture](/uploads/1/8/5/6/18566514/190709805.png)
This motion map shows the consistent decrease in the acceleration of the rock as it travels vertically.
Equations:
V = a*t + V0
V = (-9.8*1) + 24.5
V = 14.7 m/s
ΔX = (V—V0) / 2t
ΔX = (24.5—14.7) / 2*1
ΔX = 19.6 m
(this is the rock's displacement after 1 second)
Y = 1/2 g*t^2 + V0T + Y0
Y = ( 1/2*-9.8*1) + (24.5*1) + 0
Y = -4.9 + 24.5
Y = 19.6 m
V = (-9.8*1) + 24.5
V = 14.7 m/s
ΔX = (V—V0) / 2t
ΔX = (24.5—14.7) / 2*1
ΔX = 19.6 m
(this is the rock's displacement after 1 second)
Y = 1/2 g*t^2 + V0T + Y0
Y = ( 1/2*-9.8*1) + (24.5*1) + 0
Y = -4.9 + 24.5
Y = 19.6 m
Equation explanations:
V: the average velocity of the rock
V0:the initial velocity of the rock
t: the time mentioned in the question
ΔX: the displacement of the rock (the distance the rock traveled after 1 second)
(V—V0): the initial velocity subtracted from the average velocity
2t: two times the time mentioned in the problem
Y: the maximum height that the rock reaches
g: the pull that the earth elicits upon an object (gravity)
t: the time mentioned in the problem
V0: the initial velocity of the rock
Y0: the rock's initial starting point (zero, in this case)
V0:the initial velocity of the rock
t: the time mentioned in the question
ΔX: the displacement of the rock (the distance the rock traveled after 1 second)
(V—V0): the initial velocity subtracted from the average velocity
2t: two times the time mentioned in the problem
Y: the maximum height that the rock reaches
g: the pull that the earth elicits upon an object (gravity)
t: the time mentioned in the problem
V0: the initial velocity of the rock
Y0: the rock's initial starting point (zero, in this case)