Chapter 2. kinematics
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2. Acceleration
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
③ 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
① Formula 1
② Formula 2
③ Formula 3
3. Examples of Motion
⑴ Free Fall
① Definition : v0 = 0, a = g = 9.81 m/s²
② Formula 1. v = gt
③ Formula 2. s = ½ gt²
③ Formula 3. 2gh = v²
⑵ Vertical Upward Projection
① Definition : v0 > 0, a = g
② Formula 1. v = v0 + gt
③ Formula 2. s = v0t + ½ gt²
④ Formula 3. 2gh = v² - v0²
⑶ Vertical Downward Projection
① Definition : v0 > 0, a = -g
② Formula 1. v = v0 - gt
③ Formula 2. s = v0t - ½ gt²
④ 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