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Level 83

Motion in One Dimension

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A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 minutes. How fast (in m/s) is the car moving after this time? (units)
A car starts from rest and travels for 5.0 s with a constant acceleration of -1.5 m/s^2. How far does the car travel in this time interval? (units)
branch of mechanics that explains the "what" and "how" of motion
A branch of physics that focuses on force and how they relate to motion.
branch of applied mathematics dealing with motion and the forces producing motion
Displacement (delta X)
Vector drawn from the initial position to the final position
Meter (m)
SI unit Length
Direction of Displacement
Positive/negative depending on what direction it is pointing to
Magnitude of Displacement Vector
Shortest distance between the initial and final positions of the object
Displacement vs. Distance
Displacement is the shortest distance between two points, whereas distance is the path traveled by the object
Average Speed
Distance traveled divided by the time required to cover the distance
Average Speed Formula
Avg. Speed = Distance/Elapsed time
Meters per second
SI Unit for Average Velocity/Speed
Average Velocity
Dividing displacement by elapsed time
Average Velocity Formula
V= x (f) - x (i) / t(f) - t (i)
Direction of Average Velocity
Points in the same direction as displacement
Instantaneous Velocity
How fast an object is moving and direction of motion at each instant in time
Instantaneous Speed
Magnitude of instantaneous velocity
Average acceleration
a = ∆v/∆t
Average Acceleration Formula
a = v (f) - v (i) / t (f) - t (i)
SI Unit of Average Acceleration
Meter per second squared (m/s^2)
Direction of Average Acceleration Vector
In same direction as average velocity
Instantaneous acceleration
Average acceleration as change in time approaches 0
Whenever acceleration and velocity have opposite directions:
The object slows down and is said to be "decelerating"
Kinematic Equations for Constant Acceleration
(1) v (f) = v (i) + at
Rule for Using Kinematic Equations for Constant Acceleration
If three variables are known, the fourth variable can always be found
Problem Solving Insight for Kinematics
(1) Decide at start which directions are positive and which are negative
Idealized motion in which air resistance is neglected and the acceleration is nearly constant
Acceleration due to gravity
9.8 m/s/s or m/s^2 in the metric system
Displacement in Free Fall
Use "y" instead of "x"
Always a downward-pointing vector
Direction of Acceleration Due to Gravity
Symmetry in Free-Fall Motion
(1) Time required for object to reach maximum heigh equals the time for it to return to its starting point