Position, Distance, & Displacement
What is the difference between distance and displacement?
Distance is how far you’ve traveled in total.
Displacement is the final position minus the initial position, including direction.
What is speed?
Speed is the rate at which an object moves over time. It is velocity without a direction.
What is acceleration?
Acceleration is the change of velocity over time. How quickly something speeds up, slows down, or changes direction.
a = Δv/Δt
Is distance a scalar or a vector quantity?
Scalar.
A car moves at 20 m/s for 5 seconds. How far does it travel?
100 meters.
x = vt
x = (20)(5)
x = 100 meters
If a car travels 4 meters east and then 3 meters west, what is its displacement?
1 meter east.
Δx = x - x0
x0 = 3
x = 4
Δx = 4 - 3
Δx = 1
*Note that since it is positive, the direction it is going in is east.
A car drives 60 m east in 2 seconds. What is its average velocity?
30 m/s.
Velocity is displacement/change in time (Δx/Δt).
Δx = 60m
Δt = 2s
v = Δx/Δt = 60m/2s = 30 m/s
A car’s velocity changes from 10 m/s to 30 m/s in 5 seconds. What is its acceleration?
4 m/s^2.
a = Δv/Δt
Δv = v - v0
Δv = 30m/s - 10m/s
Δv =20m/s
Δt = 5s
a = 20m/s/5s
a = 4 m/s^2
Which of the following is a vector quantity: speed, velocity, or distance?
Velocity.
Speed has magnitude, distance has magnitude, velocity has magnitude and direciton.
A bike accelerates from rest to 10 m/s in 2 seconds. What is its acceleration?
5 m/s².
a = Δv/Δt
Δv = 10 m/s
Δt = 2s
a = 10/2
a = 5 m/s^2
A person runs around a 400-meter track and stops at their starting point. What is their displacement?
0 meters.
Since the person went back to the starting point, their displacement is 0 because they didn’t change position overall.
Δ x = x - x0
x = 0
x0 = 0
Δ x = 0 - 0
Δx = 0
How does velocity differ from speed?
Velocity includes direction, while speed does not.
If an object’s velocity is constant, what is its acceleration?
0 m/s².
If the velocity doesn’t change, the acceleration is zero.
True or False: Scalars have both magnitude and direction.
False. Scalars have only magnitude (amount).
A sprinter runs 100 meters in 10 seconds. What is their average speed?
10 m/s.
x = vt
x = 100 m/s
t = 10s
100 = v(10)
100/10 = v
v = 10 m/s
A hiker walks 5 m north, then 12 m east. What is the magnitude of their displacement?
13 m (use the Pythagorean theorem).
New Concept* (See explanation on the board)
A runner travels 50 meters north in 10 seconds. What is their velocity?
5 m/s north or up.
Velocity is displacement/change in time (Δx/Δt).
Δx = 50m
Δt = 10s
v = Δx/Δt = 50m/10s = 5 m/s north or up.
A ball slows down from 20 m/s to 10 m/s in 2 seconds. What is its acceleration?
-5 m/s² (negative because it is decelerating).
a = Δv/Δt
Δv = v - v0
v = 10m/s
v0 = 20m/s
t = 2s
a = (10 - 20)/2
a = -5 m/s^2
An object moves 10 m east, then 10 m west. Is its displacement a scalar or vector?
Vector. Since it has a magnitude (amount) and a direction it is a vector.
A ball is thrown upward with an initial velocity of 15 m/s and then falls back down to the person who threw it. Neglecting air resistance, what is the ball’s velocity at the highest point of its flight?
Stopped moving: 0 m/s.
New Concept*
At the highest point, gravity slows the ball down until it stops, and then it pulls the ball back down. The ball stops for a moment because gravity is pulling it back.
A train that starts from rest moves 10 m north, then 15 m south, and finally 5 m north again. What is the total distance and the displacement?
Total distance: 30 m. Displacement: 0 m.
Distance is the total amount, without considering direction. 10 + 15 + 5 = 30
Δx= xf - x0
You must add up all the times the train moves to find xf.
xf = 10 + (-15) + 5
xf = 0
x0 = 0
Δx= 0 - 0
Δx = 0
A green boat moves at 20 m/s downstream in a river with a 5 m/s current in the same direction. A red boat in different river moves at the same speed with a 2 m/s current in the opposite direction. Assume downstream is in the negative direction. What is the red & green boat’s velocity relative to their corresponding river?
Green boat’s: -25 m/s
Red boat’s velocity: -18 m/s
The green boat is moving at 20 m/s downstream, and the current is also pushing it downstream at 5 m/s. The total velocity relative to the river is -20m/s + (-5m/s) = -25 m/s
The red boat is moving at the same speed (20m/s) downstream, and the current is pushing it up at 2 m/s. The total velocity relative to the river is -20m/s + 2m/s = -18 m/s
A car accelerates at 2 m/s² for 10 seconds, starting from rest. What is its final velocity?
20 m/s.
a = Δv/Δt
a = 2 m/s^2
t = 10
2 = Δv/10
2(10) = Δv
Δv = 20 m/s
Give an example of a physical quantity that is scalar and one that is vector.
Scalar: Mass, Speed, & Time.
Vector: Displacement, Velocity, & Acceleration.
A train that starts from rest travels 60 meters at 5 m/s and then 80 meters at 10 m/s. What is its average velocity for the entire trip?
7 m/s.
See board for explanation*