Velocity Formula Derivation
Directions: As you work your way through this worksheet, draw any relevant diagrams on your
paper, show all work, and write your responses to questions in complete sentences.
Displacement is the change in position of an object.
Example 1:
-5
Example 2:
0m
-5
5
Displacement (in meters)
0m
5
Displacement (in meters):
Displacement Formula Derivation
In Physics, we use symbols and equations to represent numerical values and the relationships between
those values. Displacement is given the symbol ∆𝑥 and is the change in position of an object. Position is
given the symbol 𝑥 with subscripts to differentiate various positions. Using the symbols 𝑥𝑜 for initial
(starting) position, and 𝑥𝑓 for final position, write an equation that solves for the displacement, ∆𝑥, of an
object using the examples on the board.
(1) ∆𝒙 =
(2) Can values for displacement be both positive AND negative? __________
(3) This is what scientists call a ____________________ quantity.
(4) A value that can’t be negative is called a ____________________ quantity.
Velocity Formula Derivation
(5) Velocity measures how quickly an object is moving, and is measured in units of
𝑐𝑚
_______________ per unit of __________. (example 𝑠𝑒𝑐)
Using the data and plot from your experiment, determine an equation to solve for the velocity,
𝑣, of a buggy. Make sure you use the proper symbols for displacement, ∆𝑥, and time, ∆𝑡.
(6) 𝒗 =
**Note** We do not say that speed is negative, just that a negative speed means motion in the
opposite direction.
(7) Velocity is a term referencing an object’s speed and direction making it a ______________.
Velocity Formula Derivation
(8) On a position vs. time graph of the data, what aspect represents the speed (or velocity) of
the object?
(9) Using your newly derived formulas for average speed and displacement, solve for the final
position of an object after some time 𝑡.
Constant Velocity
(10) Think about what the term constant means and draw a velocity vs. time (𝑣 vs. 𝑡) graph of an object
moving at a constant velocity.
(11) On a velocity vs. time graph, what represents the displacement of the object? (Hint: look at the
units of each of the axes and the units of displacement as well as the equation for velocity)
(12) Draw two position vs. time (𝑥 vs. 𝑡) graphs of an object moving at a positive constant velocity, one
starting with zero initial position, and one at some non-zero initial position.
Practice Problems
Directions: Write down the symbols and values of the givens in each problem (ex. 𝑥𝑜 = 24 𝑚).
Then write down the equation you will be using before completing the computation. Please
put a box around your final answer.
Example 1:
What is the displacement of a car traveling at 50
𝑚
𝑠𝑒𝑐
after 10 seconds?
Example 2:
Solve for the position of a buggy with an initial position of 5 meters that has been travelling for 10
seconds with a velocity of 2 meters per second.
(13) How long will it take a ball to travel -25 meters if it is rolling with a velocity of -5 meters per second?
(14) What must the velocity of a spaceship be if it displaces by -20,000 miles in only 5 seconds?
𝑚
(15) A bullet shot with a velocity of 300 𝑠𝑒𝑐 will travel how far in 1 minute?
(16) What velocity will allow a train to be 1 mile behind you after only 1 minute? What is this in miles
per hour?
(17) What is the initial position of a ball rolling down a hill with a velocity of -50 centimeters per second
that ends up behind you 2 meters only 6 seconds later?
(18) How long will it take a football player that runs with a velocity of 10 yards per second to score a
touchdown when he catches the ball on his own 20 yard line? (think of the field as an inverse number
line)
(19) Draw a position vs. time graph for an object moving with a negative velocity. Explain the difference
between an object moving with a positive and one moving with a negative velocity.