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 travelled and is always +.​

​speed

​

velocity = Δ​x/Δt

​

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

velocity

​velocity vs. speed

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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.

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 rewrote this equation to better match our physics variables as:

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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".

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The "b" is replaced with x_i.

(or you may also see x_o for position at t=0s)

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.

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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.