Equations of Motion
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161 Terms
What is the dragster’s average acceleration?
26.0 m/s².
What does “from rest” mean in this example?
The dragster starts with an initial velocity of 0 m/s.
How long does the dragster accelerate?
5.56 s.
v
What is the dragster’s initial position?
0 m.
What equation is used to solve the problem?
v
Why does the v0 t term become zero?
Because the initial velocity is zero
What values are substituted into the equation?
x0=0,v0=0,a=26m/s2,t=5.56s
How is the equation simplified after substitution?
skip
What is the dragster’s final displacement?
402 m.
In what direction does the dragstar move?
In the +x direction
Why is the displacement positive?
Because the dragster accelerates to the right (+x direction)
skip
What is the goal of this slide?
To derive an equation of motion that does not contain time
What equation for position is used first?
What equation for average velocity is substituted in?
What equation is used to eliminate time?
How is the velocity equation rearranged to solve for time?
What is substituted into the position equation to remove time?
What final equation is derived on this slide?
Why is this equation useful?
It relates velocity, acceleration, and displacement without using time
What does x-x0
Displacement
What type of motion does this equation apply to?
Motion with constant acceleration
What algebra idea is used when simplifying (v+v0)(v−v0)?
Difference of squares
What does (v+v0)(v−v0) simplify to?
v2−v02
What type of motion are these equations used for?
Motion with constant acceleration
Which equation is useful when time is not given?
Which equation is useful when solving for final velocity?
Which equation is useful for displacement under acceleration?
What is the topic of this example problem?
Calculating stopping distance (displacement) of a car.
What is the car’s initial velocity in this example?
30.0 m/s.
What is the deceleration rate on dry concrete?
7.00 m/s².
What is the deceleration rate on wet concrete?
5.00 m/s².
Why is the acceleration negative in this problem?
Because the car is slowing down.
What does “coming to a halt” mean in physics terms?
The final velocity is zero.
What is the final velocity when the car stops?
0 m/s.
What additional factor is included in part (c) of the problem?
Driver reaction time.
What is the driver’s reaction time in the example?
0.500 s.
Why does reaction time matter in stopping distance problems?
Because the car continues moving before the brakes are applied.
Which motion equation can relate velocity, acceleration, and displacement without time?
What type of acceleration is assumed in this problem?
Constant acceleration.
Why is stopping distance longer on wet concrete?
Because the deceleration is smaller.
If deceleration decreases, what happens to stopping distance?
Stopping distance increases.
What unit is typically used for displacement in this problem?
Meters (m).
What does a displacement vs. time graph show?
How an object’s position changes over time.
What does the vertical axis represent on a displacement-time graph?
Displacement/position x in meters.
What does the horizontal axis represent on a displacement-time graph?
Time t in seconds.
What does the graph of an object at rest look like?
A horizontal line
Why is the graph horizontal for an object at rest?
Because the position does not change with time
What position is the object at in this example?
5 m
What is the velocity of an object at rest?
0 m/s
What does zero slope on a displacement-time graph mean?
Zero velocity.
What do linear displacement vs. time (x vs t)(x \text{ vs } t)(x vs t) graphs represent?
Constant velocity.
What does the slope of a displacement vs. time graph represent?
Velocity.
What is the formula for slope on an x vs. t graph?
What does a positive slope on a displacement-time graph mean?
Positive velocity (motion in the +x direction).
What does a steeper slope indicate on a displacement-time graph?
A greater velocity.
What is the object’s velocity in this example?
12 m/s.
In what direction is the object moving?
Positive x-direction.
Where is the object located at t=0
10 m.
What is the starting point of the graph?
(t,x)=(0,10)
What should the graph look like for constant positive velocity?
A straight line sloping upward.
What is the slope of the graph in this example?
12 m/s.
Why is the graph a straight line?
Because the velocity is constant.
What does a velocity vs. time (v vs t)(v \text{ vs } t)(v vs t) graph show?
How velocity changes over time.
What does the vertical axis represent on a velocity-time graph?
Velocity v in m/s.
What does the horizontal axis represent on a velocity-time graph?
Time t in seconds.
What does the area under a velocity-time graph represent?
Total displacement.
What does a velocity vs. time (v vs t)(v \text{ vs } t)(v vs t) graph show?
How velocity changes over time.
What does the vertical axis represent on a velocity-time graph?
Velocity v in m/s.
What does the horizontal axis represent on a velocity-time graph?
Time t in seconds.
What does the area under a velocity-time graph represent?
Total displacement
What is the velocity of an object at rest?
0 m/s.
What does the velocity-time graph look like for an object at rest?
A horizontal line at v=0
What is the area under the graph for an object at rest?
0
What does zero area under the velocity-time graph mean?
Zero displacement