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Chapter 2. kinematics

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1. Velocity and Speed

2. Acceleration

3. Examples of Motion

4. Velocity and Acceleration Experiment



1. Velocity and Speed

⑴ Velocity : Displacement per unit time, a vector quantity

⑵ Speed : Distance traveled per unit time, a scalar quantity

⑶ Average velocity : Total displacement divided by total time of travel

⑷ Instantaneous velocity : Distance traveled over an extremely short time interval divided by time

⑸ Relative velocity

① Relative velocity of A with respect to B

② Useful formula for vector calculations

Example: Finding the distance to the point of origin of thunder and lightning when lightning is seen Δt seconds before the sound of thunder occurs

○ Lightning : A flash of light. Therefore, lightning almost instantaneously reaches the observer as its speed is the speed of light, 3.0 × 108 m/s.

○ Thunder : A discharge phenomenon in the atmosphere. The speed of sound is 340 m/s.

○ Distance to the point of origin of thunder and lightning = 340 Δt (m)



2. Acceleration

⑴ Acceleration : Rate of change of velocity per unit time

⑵ Uniformly accelerated motion

Formula 1

Formula 2

Formula 3



3. Examples of Motion

⑴ Free Fall

① Definition : v0 = 0, a = g = 9.81 m/s²

Formula 1. v = gt

Formula 2. s = ½ gt²

Formula 3. 2gh = v²

⑵ Vertical Upward Projection

① Definition : v0 > 0, a = g

Formula 1. v = v0 + gt

Formula 2. s = v0t + ½ gt²

Formula 3. 2gh = v² - v0²

⑶ Vertical Downward Projection

① Definition : v0 > 0, a = -g

Formula 1. v = v0 - gt

Formula 2. s = v0t - ½ gt²

Formula 3. -2gh = v² - v0²

⑷ Projectile Motion

① Definition : 2D motion of an object (projectile) thrown upwards

○ Horizontal motion at constant speed

○ Vertical upward projection

② Initial velocity v0, with an angle θ with respect to the ground



4. Velocity and Acceleration Experiment

⑴ Experimental Procedure

① Set up the air track to be horizontal, install Photogate 1 and Photogate 2

② Ensure that the distance L between the two Photogates is significantly larger than the length d of the glider, measure L and d

③ Configure the Photogates to measure the time interval during which light is blocked as it goes from the emitter to the receiver as the glider passes through each Photogate

④ Connect a mass m to the glider with mass M, set up the apparatus, and release the glider

⑤ Measure the time interval Δt1 when the glider passes through Photogate 1, blocking the light

⑥ Similarly, measure the time interval Δt2 when the glider passes through Photogate 2, blocking the light

Figure 1. Design of the Velocity and Acceleration Experiment

⑵ Calculations

① Instantaneous velocity v1 when the glider passes through Photogate 1 : Approximated using average velocity

② Instantaneous velocity v2 when the glider passes through Photogate 2 : Approximated using average velocity

③ Magnitude of the glider’s acceleration a : Using uniformly accelerated motion formulas



Input : 2019.03.19 13:38

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