# UTPA STEM/CBI Courses/Physics (Calculus Based)/2-D Non-Rotational Motion

Course Title: Calculus Based Physics I

Lecture Topic:

Instructor: Liang Zeng

Institution: University of Texas-Pan American

## Backwards Design

[edit | edit source]**Course Objectives**

**Primary Objectives**- By the next class period students will be able to:- Know how to distinguish displacement and distance
- Know how to use calculus to analyze physics concepts mathematically and know the meaning graphically (graphic analysis): derivative of displacement (=velocity, along the tangential line), second derivative of displacement (acceleration), integral of acceleration over time (=velocity), integral of velocity over time (=displacement)
- Know how to calculate average speed
- Know how to represent directions of vectors (including force, acceleration, velocity, and displacement) with signs (positive, negative)
- Know how to apply kinematic equations for a particle under 1-D motion with constant/uniform acceleration including free fall problems (g)

**Sub Objectives**- The objectives will require that students be able to:- text
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**Difficulties**- Students may have difficulty:- Discerning the motions represented by various graphics (different functions including straight line): velocity versus time, acceleration versus time, displacement versus time
- Determining the signs for the vectors in 1-D motion including force, velocity, constant acceleration, displacement: throw downward, throw upward

**Real-World Contexts**- There are many ways that students can use this material in the real-world, such as:- Vertical:
- Vertical leap data (seconds in air) in playing basketball. How high can you jump?(picture)*
- Helicopter ascending or descending vertically
- Galileo’s free fall problem: whether two objects with different masses arrive at same time? If so, would it be the case on the Moon? (play video on the moon)*
- Simulation http://phet.colorado.edu/simulations/sims.php?sim=Lunar_Lander; http://phet.colorado.edu/simulations/index.php?cat=Motion*

- Horizontal: When you drive on some streets in the Valley: North and South (driving along Sugar from Trenton to University), West and East (driving along University from Sugar to Jackson), the section of railroad next to the bookstore, straight railroad track

- Vertical:

**Model of Knowledge**

**Concept Map**- text
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**Content Priorities****Enduring Understanding**- Difference between displacement and distance, speed and velocity (scalar and vector), average and instantaneous speed or velocity
- Match graphs with motions (position-time, velocity-time, acceleration-time)
- Velocity-time graph: Bouncing balls, velocity takes different directions so it appears down the x-axis as negative, its magnitude damps over time.
- Discern 1-D motions (for example, an incline)
- Use 1-D kinematic equations with constant acceleration: reference points (origin), position vectors, displacement vectors, initial velocity, acceleration
- Use signs for those vectors involved (displacement, velocity, acceleration)

**Important to Do and Know**- How to solve problems where acceleration is not constant (eg. a bus ride or driving with stopping and starting at lights – either split the entire motion into different segments and solve with those kinematic equations, or integrate a(t) from the original formula a(t)= d2x/dt2)
- Review relative velocity (traffic flow: same direction: v1-v2; opposition direction: v1-(-v2) because v2 is in opposite direction – cars approaching one another seem to go very fast)
- The physics laws are invariant in different coordinate systems, therefore, you are free to choose a coordinate system that is most convenient for problem solving. Whether you choose upward or downward as positive sign, it will not change the essential meaning of the final result. Only the mathematics expressing the final result looks slightly different. For example, velocity takes a positive or negative signs.

**Worth Being Familiar with**- How to derive 1-D kinematic equations from Newton’s second law of motion, if acceleration is constant

**Assessment of Learning**

**Formative Assessment**- In Class (groups)
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- Homework (individual)
- Pay attention to the following new units: m/s, km, 1 mi = 1.609 km
- Self-reading Chapter 2 in the textbook
- (Graphical analysis: position/time graph: Knight, Jones, Field College Physics page 64 #13). The figure shows the position graph of a particle.
- Draw the particle’s velocity graph for the interval 0 s ≤ t ≤ 4 s.
- Does this particle have a turning point or points? If so, at what time or times?

- (Graphical analysis: velocity/time graph: Knight, Jones, Field College Physics page 65 #16). The figure shows the velocity graph of a train that starts from the origin at t = 0 s.
- Draw the position and acceleration graphs for the train.
- Find the acceleration of the train at t = 3.0 s.

- (Graphical analysis: position/time graph: Knight, Jones, Field College Physics page 64 #13). The figure shows the position graph of a particle.

- In Class (groups)

- (1D motion upward: Serway 7th edition page 49 #39). A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand.
- With what initial velocity were the keys thrown?
- What was the velocity of the keys just before they were caught?

- (1D motion downward: Serway 7th edition page 49 #38). A ball is thrown directly downward, with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does the ball strike the ground?
- (1D motion free fall: Serway 7th edition page 50 #45). A freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?
- (1D motion horizontal: Serway 7th edition page 48 #25). The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration of -5.60 m/s2 for 4.20 s, making straight skid marks 62.4 m long ending at the tree. With what speed does the car then strike the tree?

- (1D motion upward: Serway 7th edition page 49 #39). A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand.

**Summative Assessment**- text
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## Legacy Cycle

[edit | edit source]**OBJECTIVE**

By the next class period, students will be able to:

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The objectives will require that students be able to:

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**THE CHALLENGE**

You are part of a mission to land a polar lander near the Martian North Pole in order to investigate the possibility of discovering ice at the pole. The lander falls in two segments in its final stage of landing: free fall followed by a parachute deployment. Assume the probe is close to the surface, so the Martian gravitational acceleration constant is 3.00 m/s2. The lander is initially moving vertically downward at 200 m/s at a height of 20 000 m above the surface. Neglect air resistance during the free-fall phase. The net deceleration rate of the lander (including the Martian gravitational acceleration) from the time the parachute opens to the time it reaches a velocity of 20 m/s is 3.65 m/s2 (20 m/s is the maximum speed the lander can safely land on the Martian surface, see figure). At what height above the Martian surface should the lander deploy its parachute?

**GENERATE IDEAS**

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**MULTIPLE PERSPECTIVES**

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**RESEARCH & REVISE**

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**TEST YOUR METTLE**

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**GO PUBLIC**

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## Pre-Lesson Quiz

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## Test Your Mettle Quiz

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