Velocity, Acceleration, and Free Fall


What do the following variables represent?  What units are commonly used for them?

Variable                                        Units

df =

t =

vi =

vf =

a =

g =


Use these formulas to solve the following problems.  Use g = 10 m/s

Constant velocity:


Accelerated Motion(Arthur, Vickie, Dickie, and Dickie Jr.)




  1. Speed is the rate at which what happens?
  2. What is the difference between speed and velocity?
  3. Acceleration is the rate at which what happens?
  4. What is the meaning of free fall?
  5. Toss a ball upward.  What is the change in speed each second on the way up?  On the way down?
  6. What does the slope of the curve on a distance vs. time graph represent?
  7. What does the slope of the curve on a velocity vs. time graph represent?
  8. Using v=∆d/∆t:

 a)  Calculate the average speed (in km/h) of Charlie, who runs to the store 4 km away in 30 minutes.

b)  Calculate the distance (in km) that Charlie runs if he maintains this average speed for 2 hours.

9.  Using a=∆v/∆t:   Calculate the acceleration of a car (in km/h•s) that can go from rest to 100 km/h in 10s.

10.  How long will it take a car with an acceleration of 5 km/h•s to reach a speed of 80 km/h if it starts from rest?

11.  How long will it take a car with an acceleration of 5 m/s2 to reach a speed of 180 km/h? (Hint:  Watch your units!)





Position vs. Time graph





12. What interval(s) show zero velocity?

13.  Describe what is happening between interval 1 & 2.


Velocity vs. Time graph






14.  At what time interval(s) was acceleration zero?

15.  An object is dropped from rest and falls freely.  After 6 seconds, calculate its instantaneous speed, average speed and distance fallen.

16.  A dragster going at 15m/s north increases its velocity to 25m/s north in 4 seconds.  What is its acceleration during this time interval?

17.  A car going at 30 m/s undergoes an acceleration of 2m/s2 for 4 seconds.  What is its final speed?  How far did it travel while it was accelerating?

18.  If a salmon swims straight upward in the water fast enough to break through the surface at a speed of 5 meters per second, how high can it jump above the water?

19.  At a party, Stu P. Dity celebrates by shooting a bullet vertically into the air. The

          bullet’s initial velocity is 1.00 x 102 m/s.

a. How high will the bullet go before falling back to the ground?

b.  How long will the bullet be in the air?

     c.  How fast will it be going when it hits Stu back on the ground?


Vector and Projectile Motion Review

In addition to using the formulas from the 1st section list the following formulas that help with vector addition.


The Pythagorean Theorem    


Tan θ =                                       θ =

Sin θ =                                        θ =

Cos θ =                                       θ =


1.  Why is speed classified as a scalar quantity and velocity classified as a vector quantity?

2.  At the instant a horizontally pointed cannon is fired, a cannonball held at the cannon’s side is released and drops to the ground.  Which cannonball strikes the ground first, the one fired from the cannon or the one dropped?

3.  Use the following to illustrate the triangular method of vector addition: 

What is the magnitude and direction of an 80 km/h airplane flying in a 60 km/h crosswind?

4.  A projectile is launched at an angle into the air.   Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?

5.  At what point in its path does a projectile have minimum speed?

6.  In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant while the vertical component changes?

7.  Calculate the resultant velocity of an airplane that normally flies at 200 km/h if it encounters a 50 km/h tailwind.  If it encounters a 50 km/h headwind.

8.  Calculate the resultant of the pair of velocities 100 km/h north and 75 km/h south.  Calculate the resultant if both of the velocities are directed north.

9.  Calculate the magnitude of the horizontal and vertical components of a vector that is 100 units long and is oriented at 45˚.

10.   The launching velocity of a projectile is 20 m/s at 53˚ above the horizontal.  What is the vertical component of its velocity at launch?  Its horizontal component of velocity?  Neglecting air friction, which of these components remains constant throughout the flight path?  Which of these components determines the projectile’s  time in the air?

11.  A projectile is launched straight up at 141 m/s.  How fast is it moving at the top of its trajectory?  Suppose it is launched upward at 45˚ above the horizontal plane.  How fast is it moving at the top of its curved trajectory?

12.  A girl is playing shuffleboard on an ocean liner that travels due north at 3 m/s.  She makes a starboard shot (toward the east), relative to the deck, of 4 m/s.  What is the velocity of the puck relative to the stationary stars?

13.  Harry accidentally falls out of a helicopter that is traveling at 100 m/s.  He plunges into a swimming pool 2 seconds later.  Assuming no air resistance, how high was the helicopter and what was the horizontal distance between Harry and the swimming pool when he fell from the helicopter?

14.  Harry and Angela look from their balcony to a swimming pool below that is 15 m from the bottom of their building.  They estimate the balcony is 45m high and wonder how fast they would have to jump horizontally to succeed in reaching the pool.  What is your answer?

15.  A girl throws a slingshot pellet directly at a target that is far enough away to take one-half second to reach.  How far below the target does the pellet hit?  How high above the target should she aim?

16.  A boy on a 20 m tower throws a ball a distance of 60 m off the tower.  At what speed, in m/s, is the ball thrown?

17.  A shiny new sports car sits in the parking lot of a car dealership.  Above is a cargo plane, flying horizontally at 50 m/s.  At the exact moment the plane is 125 m directly above the car, a heavy crate accidentally falls from its cargo doors.  Relative to the car, where will the crate hit?





Newton’s Laws and Gravity

List Newton’s three laws




List the formula for Universal gravitation




List the formula for circular acceleration


List the formula for circular force (or centripetal force)



Review homework, practice test and test


Momentum, Impulse, Conservation of Momentum

List Formulas:



Impulse/change in momemtum


Conservation of momentum








1. What is momentum?

2.  When the average force of impact on an object is extended in time, does this increase or decrease the impulse?

3.  What is the relationship between impulse and momentum?

4.  In a car crash, why is it advantageous for an occupant to extend the time during which the collision is taking place?

5.  The text state that if no net force acts on a system then the momentum of that system cannot change.  It also states there is no change in momentum when a rifle is fired.  Doesn’t the fact that a bullet undergoes a considerable change in momentum as it accelerates along the barrel contradict this? Explain.

6.  What does it mean to say that momentum is conserved?

7.  Distinguish between an explosive event, elastic and inelastic collision.


Use the momentum practice problems and class work to prepare for this portion of the midterm.