Chapter 2: Linear Motion. Chapter 3: Curvilinear Motion

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2 Chapter 2: Linear Motion Chapter 3: Curvilinear Motion

3 Linear Motion Horizontal Motion - motion along x-axis Vertical Motion (Free-Falling Bodies) motion along y-axis

4 Equation for Uniformly Accelerated Linear Motion S Displacement Vo Initial Velocity a acceleration V Final Velocity t time elapsed

5 Example 1: Cars A and B approach each other on a straight road from points 457 m apart. Car A has an initial speed of 20 m/s and is decelerating at the rate of 0.4 m/s 2. Car B has an initial speed of 5 m/s and is accelerating at the rate of 0.3 m/s 2. (a) When will the cars meet? (b) How far will car A have travelled when they meet? (c) What will the speed of car A and car B be when they meet?

6 Example 2: Two cars start form rest at the same instant, with care A initially at some distance behind car B. Car A has a constant acceleration of 3.50 m/s 2 and car B an acceleration of 2.15 m/s 2, Car A overtakes car B after car B has moved 40.2m (a) How much time does it take car A to overtake car B? (b) How far was car A behind car B initially? (c) What is the speed of each car when car A overtakes car B?

7 Example 3: A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?

8 Example 4: Two cars start from rest from a gasoline station at the same instant. They travel in the same direction, both of them accelerating. The first car has an acceleration whose magnitude is 4.5 m/s 2. The second car s acceleration has a magnitude of 3.0 m/s 2. Assuming straight-line motion: (a) How much time passes until they are 2.5 km away from each other? (b) How far has the first car traveled then? (c) How far has the second car traveled then?

9 Example 5: A police car hidden at an intersection observes a car that is moving with a constant speed of 40 m/s. The police immediately accelerated at 8 m/s 2 and followed the car when the police was 50 m behind the car. (a) When did the police catch up with the car? (b) How far from the intersection did the police catch up with the car? (c) How fast was the police car traveling by the time it caught up by the car?

10 Free-Falling Bodies (Constant Acceleration) S Displacement Vo Initial Velocity g gravity V Final Velocity t time elapsed

11 Example 6: A missile is launched into the air at an initial velocity of 80 m/s. it is moving with constant velocity until it reached 1000 m, when the engine fails (a) How long does it take it to reach 1000m? (b) How high does the missile go? (c) How long does it take for it to fall back to the earth? (d) How long does it stay in the air? (e) How fast is itgoing when it hits the ground?

12 Example 7: Suppose a small ball is thrown vertically upward. It returns to its point of release with a speed of 1960 cm/s. in the absence of air resistance: (a) How long did it take the ball to reach its maximum height? (b) To what maximum height did the ball rise? (c) What was the ball s velocity 1000 cm above its point of release?

13 Example 8: A ball is thrown vertically upwards, with an initial speed of 50 ft/s, from the top of an 80-ft tall school building. At the same instant, a student is running on the ground at a distance of 100 ft from the building. (a) What is the maximum height (with respect to the ground) that the ball attains? (b) What is the speed of the ball when it reaches the bottom of the building? (c) What must the average speed of the student be if he is to catch the ball at the bottom of the building?

14 Example 9: A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at 4 m/s 2 until it reaches an altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard resistance (a) How long was the rocket above the ground? (b) What is the maximum altitude? (c) What is the velocity just before it collides with the ground?

15 Example 10: A rock is dropped from rest into a well. The sound of the splash is heard 4s after the rock is released from rest. How far below to top of the well is the surface of the water? (Speed of sound in air at ambient temperature is 336 m/s).

16 Example 11: A rock is shot up vertically upward from the edge of the top of the building. The rock reaches its maximum height 2 sec after being shot. Then, after barely missing the edge of the building as it falls downward, the rock strikes the ground 8 sec after it was launched. Find; (a) Upward velocity the rock was shot at (b) The maximum height above the building the rock reaches (c) Height of the building