Velocity, x vs. t graphs, and equations

Multiple Choice

A car moved from x₁ = 80 mi to x₂ = -40 mi in 4 hours.

What was the car's velocity?

• 30 mph

• -30 mph

• 120 mph

• -10 mph

velocity

​velocity = displacement / time elapsed

​

or

​

v = Δ​x/Δt

Multiple Choice

A car moved from x₁ = 80 mi to x₂ = -40 mi in 4 hours.

What was the car's speed?

• 30 mph

• -30 mph

• 120 mph

• -10 mph

Multiple Choice

Are speed and velocity the same thing?

• Yes, the words speed and velocity can be used interchangeably.

• No, speed is always positive, but velocity can be both positive or negative.

​

speed = path length/Δ​t

​

path length is the total distance traveled and is always +.​

​speed

​

velocity = Δ​x/Δt

​

if Δ​x (displacement) is negative, then velocity is negative.

velocity

​velocity vs. speed

Multiple Choice

The graph shows the motion of a football player during 20 seconds.

What is the player's position at the point marked with a triangle?

• The player is at the 10 yard line.

• The player is at the 4.5 yard line.

• The player is at the 45 yard line.

• Cannot be determine from this graph.

Multiple Choice

How far did the player travel by the time they reached the position marked by the triangle?

• The player traveled 10 yards.

• The player traveled 35 yards.

• The player travelled 45 yards.

• Cannot be determine from this graph.

Multiple Choice

What is the total distance traveled by the football player in the 20 seconds of play?

• 0 yards

• +5 yards

• -5 yards

• 85 yards

Draw

Circle the point or points on the graph when the player is moving the fastest.

Draw

Is the player ever standing still? If no, then draw an X through the graph.

If yes, then circle the point or points where the player is at rest.

​Equation of a straight line

position = vt + b

Recall that the equation of a straight line is y = mx + b. We can rewrite this equation to better match our physics variables as:

Some text here about the topic of discussion

We replaced "y" with "position" because our position is on the y-axis of the graph. We replaced "m" with "v" for velocity, because the slope of the line is the velocity of the object. We replaced the "x" with a "t" because the x-axis of the graph is time.​

​Equation of a straight line... refined

x_f = v_xt + x_i

It's cumbersome to write out the word position. If we are referring to an object moving horizontally, we'll instead use an "x" with a subscript "f", which stands for "final".

Some text here about the topic of discussion

The "b" is replaced with x_i which is the initial position of the object.

(you may also see x_o instead of x_i )

The v with the subscript x just lets us know very specifically that the object's velocity is horizontal.

​For something moving vertically...

y_f = v_yt + y_i

​Sometimes objects move up and down. In that case, replace the x's with y's, since the object is moving on the y-axis of our world.

Some text here about the topic of discussion

Multiple Select

The motion of an object is represented by the equation

x = (5.0 m/s)t

Which statement(s) is/are TRUE?

• The object's velocity is 5.0 m/s.

• The object's velocity is -5.0 m/s.

• The object is at rest at zero seconds.

• The object's position is 5.0 meters at 1 second.

Multiple Select

The motion of an object is represented by the equation

x = (-3.5 m/s)t

Which statement(s) is/are TRUE?

• The object's velocity is 3.5 m/s.

• The object's velocity is -3.5 m/s.

• The object is at rest at zero seconds.

• The object's position is 3.5 meters at 1 second.

Multiple Choice

A train is moving 15 m/s. How far will it move in 10 seconds?

• 15 meters

• 150 meters

• 1.5 meters

• Not enough information is given to solve.

Multiple Choice

A train is moving 15 m/s. How far will it move in 10 minutes?

• 150 meters

• 600 meters

• 9000 meters

• Not enough information is given to solve.

Multiple Choice

You ride your bike to your friend's house 3 km away saving 12 ounces of gasoline from being burned and adding to the climate crisis! You arrive at the house in 17 minutes. What is your speed in km/min?

• 5.7 km/min

• 0.2 km/min

• 36 km/min

• 612 km/ min

Draw

Write an equation for the bike-riding example. Hint: There are many ways to represent this motion with an equation. Recall that you drove 3 km in 17 minutes.