One Dimensional Motion

Kinematics: 1-d Motion Review

Exam Review Day 1

Kinematic Equations

We NEED these to help us solve problems involving motion and the relevant values: distance/displacement, velocity, acceleration, and time.

It is important to distinguish between initial and final using subscripts.

Average Velocity

• Simply distance over time

• Regardless of incremental changes (accelerations), this value gives us the most applicable measurement for who wins a race, and similar questions.

Avg. Velocity: Graphs

• Find the slope!

• Velocity from 0 to 8 sec = 0 (not moving)

• What about from 8 to 16 seconds?

Avg. Velocity: Graphs

• From 8 to 16 seconds, the slope is -12 meters over 8 seconds.

• Therefore, the average velocity is -1.5 m/s.

• Ok one more, what's the average velocity for the WHOLE graph?

Displacement? huh?

• Measured as CHANGE in initial and final position.

• What is the total displacement for this graph?

Displacement = $\Delta x=x_f-x_i$  

•  $x_f=-6$  
  

•  $x_i=12$  
  

•  $\Delta x=-18$  

• However, the total distance traveled can be found as (from 12) down 27, then up 9 more.   

• Total distance = 36 meters (it's a scalar so it must be positive)

Avg. Velocity: Graphs

• The whole graph is 24 seconds.  

• Velocity is displacement over time  $\frac{displacement}{time}=\frac{\Delta x}{\Delta t}=-\frac{18m}{24s}=-0.75\ \frac{m}{s}$  

Multiple Choice

What is this graph representing?

• Constant Speed

• Acceleration

• Deceleration (negative acceleration)

• No motion

Multiple Choice

How long will it take you to get to Panama City 3000 m away, if you average 30.0 m/s for the trip?

• 100 s

• 90,000 s

• 0.01 s

• 3 s

Multiple Choice

Which graph shows a person jogging away at a constant pace?

• A

• B

• C

Multiple Choice

The famous skier, Walajones, leaves a 22.13 m high cliff with a horizontal velocity of 40 m/s. How long is the skier in the air?

• 10.54 s

• 3,400 s

• 5.23 s

• 2.125 s

Multiple Choice

Jerry walked from home to school, then from the school to the park. What is his total displacement?

• 2 km

• 5 km

• 8 km

• 10 km

Multiple Choice

A person walks 50 meters directly north, stops, and then travels 32 meters directly south. What is their displacement?

• 82 meters

• 18 meters

• 28 meters

Multiple Choice

The speed of the vehicle between points A-B is...

• 12m/s
• 8m/s
• 10m/s
• 16m/s

Velocity-Time Graphs

• Plot velocity over time

• SLOPE is acceleration

• AREA is displacement

Choosing Kinematic Equations

Examine the values given in the problem. Essentially, for 1-step problems, we use the equation where only 1 variable is unknown. This allows us to solve for that unknown.

SO which is it for this one?

Choosing Kinematic Equations

We know both initial AND final velocity and displacement. Therefore, we should use D. It is a SINGLE step because we just want the acceleration.

Which kinematic equation?

• Given initial velocity.

• But...do we know acceleration?

Which kinematic equation?

• YES...acceleration due to gravity is CONSTANT (-9/8 m/s/s).

• We also know that, at the peak, the "final" velocity is 0.

• That leads to equation D.

Sample Question 1

• Speed (v) = 2 m/s

• Acceleration unknown, but constant

• Displacement is 3 m

• Find the time.

• 2-step problem for sure, go for it!

Start with pink equation. Find the accel. Plug in to find time (purple arrow).