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Estimating Speed According to a rule-of-thumb, every five seconds between a lightning flash and the following thunder gives the distance of the storm in miles. Assuming that the flash of light arrives in essentially no time at all, estimate the speed of sound in m/s from this rule.

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**Kinematics in One Dimension**

MECHANICS comes in two parts: kinematics: motion (displacement, time, velocity) x, t, v, a dynamics: motion and forces x, t, v, a, p, F

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**Kinematics in One Dimension**

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**Displacement - difference in location; length**

consider a coordinate system (for 1-D, it is a number line or single axis). any difference in locations is a displacement

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**Velocities Average velocity - over the trip, or distance, or time**

Instantaneous velocity - right now speed

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**d = 2100 km + 1800 km = 3900 km v = d/t = 881 km/hr**

An airplane travels 2100 km at a speed of 800 km/h, and then encounters a tailwind that boosts its speed to 1000 km/h for the next 1800 km. What was the total time for the trip? What was the average speed of the plane for this trip? d = 2100 km km = 3900 km v = d/t = 881 km/hr

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**Acceleration How to express a change in velocity?**

Again, two kinds of acceleration:

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**Kinematics defined by - x, t, v, a**

x displacement t time v velocity a acceleration

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**An automobile is moving along a straight highway, and**

the driver puts on the brakes. If the initial velocity is v1 = 15.0 m/s and it takes 5.0 s to slow to v2 = 5.0 m/s, what is the car’s average acceleration?

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**From the definition for average acceleration:**

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**Motion at Constant Acceleration**

kinematics - x, t, v, a How are these related? For simplicity, assume that the acceleration is constant: a = const

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Consider some acceleration: The resulting velocity:

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For a constant acceleration: Realize a displacement:

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**How about an equation of motion without time?**

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Equations of Motion

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**Try It! Consider an airport runway. A light aircraft must reach**

a speed of 100 km/hr (27.8 m/s) to lift off. It can accelerate at 2.00 m/s2. A) If the runway is 150 m long, can the airplane take off? B) If it cannot take off, how long of a runway would be required?

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**Try It! Doing part B) first:**

For part A), runway length is not sufficient.

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**Problem Solving Read the problem Draw a diagram**

List what is known and what is wanted What physics principles are appropriate List relevant equations and their applicability (may have to derive the best equation) Calculate the requested quantity Make an estimate - are the results reasonable Balancing units can serve as another check

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**A car speeding at 80 mi/hr passes a stationary police car.**

The police car immediately gives pursuit. If the speeding car remains at a constant velocity, and the police car can maintain a constant acceleration of 4.5 m/s2, how long is required to catch the speeder and how fast is the police car traveling? vs = 80 mi/hr = 35.8 m/s ap = 4.5 m/s2 = 10.0 mi/hr-s

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**Seeking to catch the malefactor:**

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**If the one-dimensional motion is vertically oriented…**

Try a = g (9.807 m/s2 or ft/s2 , down) Galileo derived kinematics based on experiments. Concerning the motion of falling objects, all objects fall with the same constant acceleration In the absence of air resistance, regardless of the size or mass, all objects fall with the same acceleration g.

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**A ball is dropped from a tower that is 70.0 m in height.**

How far will it have fallen in 1.00 s, s, and 3.00 s? How long will it take to reach the ground?

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**A person throws a ball upward with an initial velocity**

of 15.0 m/s. How long will the ball take to be caught?

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