Do Now warm-up prompt

Average Speed - how much distance an object covers per unit time

Sheldon from the Big Bang explains physics

Why is Science Important? from Alom Shaha on Vimeo.

“The most incomprehensible thing about the world is that it is comprehensible.”

— Einstein

Unit I - Mechanics

Study of the relationship between force and motion

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I. Kinematics

Mathematical methods of describing and predicting motion

Describe motion by using:

A) Average Speed

Average Speed of 120 miles per hour can also be written ... 120 miles/hour

per = divided by

Could mean travelled 120 miles in one hour, OR ... 60 miles in 1/2 hour (30 minutes), OR 15 miles in 7.5 minutes.

Avg. Speed - how much distance an object covers per unit time

1) Units: m/s, km/hour, miles/hour

Average Speed = Δd/Δt

Distance

Speedometer icon Meter stick

(meter ≈ 1 yard)

(km ≈ .6 miles)

Time

Stopwatch icon

seconds, minutes, hours

Ex 1

Given

An object travels 5 meters in 2 seconds.
Find: its speed.

↓

Speed = Δd/Δt
= 5 m / 2 sec

= 2.5 m/s

Ex 2

Given

An object moves at a rate of 3 m/s for 1.5 seconds.
Find: how far did the object move?

↓

Speed = Δd/Δt →
3 m/s = d / 1.5 sec

d = 4.5 m

Muybridge animated race horse
Photos made by Eadweard Muybridge (1830-1904). Animation by User Waugsberg. Public Domain.

Ex 3

Given

An object moves at a rate of 4 m/s over a distance of 10 meters.
Find: how long did it take to travel that distance?

↓

Speed = d/t →
4 m/s = 10 m/t (Cross Multiply)

(4 m/s)t = 10 m (Divide by 4)

t = 2.5 seconds

B) Motion Plots

(a.k.a. Motion Diagrams)

Businessman pointing

Position vs. Time Plot

Position vs time plot

Speed from 0 to 2 seconds?

Speed = Δd/Δt
= 5 m / 2 sec

= 2 m/s

Speed from 2 to 4 seconds?

Speed = Δd/Δt
= 5 m / 2 sec

= 2 m/s

Speed from 4 to 6 seconds?

Speed = Δd/Δt
= 5 m / 2 sec

= 2 m/s

Does the object travel faster or slower from 6 to 8 seconds?

Slower Speed

(smaller change in d during the same time)

Compare speed from 6 to 8 sec with speed from 8 to 9 sec.

Same Speed, Same Slope

What kind of motion produced this plot?

Curved position vs time plot
Curved position vs time plot, steepening slope

Increasing Speed

Motion map showing increasing spacing
Displacement

Equations

NYSSLS Regents Practice · Kinematics · Patterns in Data

Sprint Timing Gates

A track coach set up timing gates along a straight track to study a runner’s training sprint. The runner’s distance from the starting line was recorded every 2.0 seconds, as shown in Table 1.

Table 1: Runner Position Data

Time (s)02.04.06.08.010.0
Distance (m)08.016.024.036.048.0

Which statement best describes the runner’s motion based on the data?

▶ Want a challenge? Open 6 more Regents-style questions  (harder · mixed formats)

Challenge score: 0 / 6

Multiple choice

C1. Which graph best represents distance versus time for the runner?

Substitute values

C2. Substitute numerical values into a mathematical representation that can be used to determine the runner’s average speed for the entire 10.0 seconds. Then calculate the average speed.

v = m s = m/s
Support or Refute · Justify

C3. A student makes the following claim.

Claim: The runner’s speed from 6.0 s to 10.0 s was 1.5 times her speed from 0 s to 6.0 s.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Determine the value

C4. If the runner keeps the same speed she had from 6.0 s to 10.0 s, determine the time at which she crosses the 100.-meter mark.

t = s
Multiple choice

C5. A second runner’s distance–time line is parallel to the first runner’s line from 0 to 6.0 s but starts at 10 m instead of 0 m. Which conclusion is correct for that interval?

Constructed response

C6. Table 1 seems to show the runner changing speed suddenly at exactly 6.0 s, but a real runner must speed up over some time. Describe one change to the coach’s data collection that would give better evidence of how the runner’s speed actually changed, and explain why it would help.