Motion Terms - Speed (AP) - Kinematics

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

— Einstein

Unit I - Mechanics

Study of the relationship between force and motion

I. Kinematics

Mathematical methods of describing and predicting motion

Motion Plots (a.k.a. Motion Diagrams) — plots of motion information & equations

II. How Do We Measure Motion?

III. Measuring Motion?

Distance

(meter ≈ 1 yard)

Time

(seconds)

Direction

A) Speed

Speed - distance an object covers per unit time

1. Speed = distance / time

a) Units - m/s, km/hour, miles/hour

Ex 1

Given

A student on a merry-go-round moves in a circular path with a radius of 3.5 m once every 8.9 secs.
Find: the student's average speed and average velocity.

↓

Speed = d/t
= [2π(3.5 m)] / 8.9 sec

Speed = 2.5 m/s

Average velocity for a single trip around the merry-go-round?

0 m/s

Ex 2

Given

Cars A and B are 400. m apart. Car A travels 35. m/s east on a collision course with car B, which travels 15. m/s west.
Find: how long will it take for the cars to collide?

↓

When the cars collide, total d = 400. m

d = Speed × time →
400. m = 35. m/s(t) + 15. m/s(t) = 50. m/s(t)

t = 8.0 s

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

Ex 3

Given

A car travels 250 km at an average speed of 95 km/h, stops for lunch for 1.0 hour, and then travels 250 km at a rate of 55 km/h.
Find: the car's average speed in m/s.

↓

Speed = total d / total time total d = 500 km

time 1 = 250 km / 95 km/h
= 2.6 hr time 2 = 1 hr time 3 = 250 km / 55 km/h = 4.5 hr

Total t = 8.1 hours Speed = 500 km / 8.1 hr = 62 km/hr

62 km/hr × (1000 m/km) × (1 hr/60 min) × (1 min/60 sec)

≈ 17 m/s

Ex 4

Given

A cop riding 100 mph pursues a criminal travelling 85 mph. It takes the cop 15 minutes to catch up with the criminal.
Find: what distance, in miles, originally existed between the cop and the criminal when the pursuit began?

↓

d = 15 mph × .25 hrs

d = 3.8 miles

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. A student rides a merry-go-round and makes exactly one full trip around. What is the student's average velocity for that trip?

2. Two cars are 300. m apart and drive toward each other at 20. m/s and 10. m/s. How long until they collide?

3. A car drives 100 km at 50 km/h, stops 1.0 h for lunch, then drives 100 km at 100 km/h. What is its average speed for the whole trip?

4. A police car at 90 mph chases a car going 60 mph and catches it in 20 minutes. How far apart were they at the start?

5. A car travels at 36 km/h. What is this speed in m/s?

Displacement →