Vector Basics & 1D Motion
An object moves 4 units to the right and then 3 units to the left. What is the magnitude of its total displacement?
1 unit, because in one dimension, vectors with opposite directions have opposite signs
On a velocity vs. time graph, at what point is an object at rest?
Every time t where the velocity Vx is zero (crosses the horizontal axis)
A car speeds up from 20 m/s to 40 m/s in 5 seconds. What is its acceleration?
4 m/s^2
A student walks toward the front of a bus moving east at constant speed. Why does a stationary observer see the student moving faster than the bus?
The student's velocity relative to the observer is the velocity of the bus plus the velocity of the student relative to the bus
A rock is thrown horizontally at 10 m/s from a 20 m high cliff. How far from the base of the cliff does it hit the ground?
20 m
Compare the speeds of three objects moving with horizontal velocities of v, -v/3, and -3v. Which object is moving the fastest?
On a velocity vs. time graph, how can you identify intervals where the speed is increasing?
When the magnitude of the velocity is moving away from the zero-axis.
A ball dropped from a building falls 1 floor in 1 second. How many total floors will it have fallen after 3 seconds, assuming constant acceleration?
9 floors
Car A moves at 30 m/s and Car B moves at 10 m/s in the same direction. What is the velocity of Car B relative to Car A?
−20 m/s
A cart leaves a track 0.40 m above the floor. What determines the time it takes to hit the floor?
The vertical height of the track and the acceleration due to gravity
If Vector C is the sum of parallel vectors A and B, and the magnitude of B is greater than the magnitude of C, what must be true about the directions of A and B?
They must have opposite directions.
If a car starts from rest and you graph its x vs t^2, a straight line indicates what type of motion?
The car is speeding up at constant rate (constant acceleration)
In Case 1, a toy is caught at its highest point. In Case 2, it falls back to its start. Which case has a greater average velocity magnitude during free-fall?
Case 1, because the toy has a greater displacement relative to the time spent in the air
A river flows east at 5 m/s. A boat moves west at 10 m/s relative to the water. A passenger walks east at 5 m/s on the boat. What is the passenger's velocity relative to the shore?
stationary (0 m/s)
A block leaves a track at a 30º angle with a speed of 3.0 m/s. What is its speed at the highest point of its motion?
2.6 m/s (This is the horizontal component, 3.0cos30º)
A car is at rest from t=0 to t=1 s. It reaches x=40 m at t=5 s and x=80 m at t=10 s. Why is the average velocity lower during the first 5 seconds than the last 5 seconds?
Because the car was at rest for part of the first time interval
On a position vs. time graph, how do you determine when two objects have the same velocity?
When the slopes of their position-time curves are equal.
What is the mathematical expression for the time it takes for a car accelerating at aB from rest to catch a car moving at a constant velocity vA?
t=2vA/aB.
A block slides at a constant speed while launching a ball straight up. Where will the ball be relative to the launcher when it reaches its maximum height?
Directly above the spring launcher
A ball is thrown horizontally off a 10 m building and lands 3 m away. What was its initial horizontal speed?
2.14 m/s
Looking at a table of motion, how can you tell if an object changed direction?
By observing if the sign of the velocity changes from positive to negative (or vice versa).
How do you find the horizontal position of an object at t=9 s if you are given its initial position at t = 0 and a velocity - time graph?
Add the initial position to the area under the velocity - time graph from t = 0 to t= 9s.
If an athlete runs between intervals with different speeds and directions, how do you find the transition with the greatest magnitude of change in velocity?
Calculate Δv=vf−vi for each transition; the largest value (ignoring sign) is the greatest magnitude
Why is a passenger on a boat moving 10 m/s west in a 5 m/s eastward river considered stationary relative to the shore if they walk 5 m/s east?
Because the boat moves at 5 m/s west relative to the shore, and the passenger moves 5 m/s east relative to the boat, cancelling the motion
If air resistance is neglected, what happens to the horizontal velocity of a projectile throughout its flight?
It remains constant