UAM HORIZONTAL DIMENSION GRADE 9 LEVEL.pptx

UNIFORMLY ACCELERATED MOTION

1. Have you ever observed how a car accelerates on a straight road? What happens if there is no friction or air resistance?

2. Uniformly Accelerated Motion: Horizontal Dimension

3. LEARNING OBJECTIVES Explain the concept of uniformly accelerated motion in the horizontal dimension. Solve problems involving uniformly accelerated motion in the horizontal dimension. Appreciate the significance of acceleration in understanding real-world motion and technological advancements.

4. UNIFORMLY ACCELERATED MOTION Uniformly Accelerated Motion (UAM) refers to the motion of an object in which the acceleration remains constant over time. This means that the velocity of the object changes at a steady rate. In the horizontal dimension, this occurs when there is no external force (like friction) acting on the object except for a constant applied force.

5. CHARACTERISTICS Constant Acceleration - The acceleration remains uniform, meaning it does not change over time. Velocity Changes Linearly - The object's velocity increases or decreases at a constant rate. Position Changes Quadratically - Displacement follows a quadratic relationship with time due to constant acceleration.

6. Independence of Horizontal and Vertical Motion - In two-dimensional motion, horizontal motion is treated separately from vertical motion. Applies to Various Real-Life Situations - Examples include vehicles accelerating on a highway, athletes sprinting, and projectile motion in sports. CHARACTERISTICS

7. SAMPLE PROBLEM A car is moving at an initial velocity of 10 m/s and accelerates uniformly at 2 m/s² for 12 seconds . Find: The final velocity The total distance traveled

8. Using the kinematic equation: v f = v i + at Where: v i =10 m/s (initial velocity) a= 2 m/s² (acceleration) t= 12 s (time)   v f ​= 10 m/s + (m/s² × 12 s) v f = 10 m/s + 24 m/s v f = 34 m/s Step 1: Find the Final Velocity

9. Using the kinematic equation: d = v i t + a Where: d = distance (m) ​v i =10 m/s a = 2 m/s² t=12 s   d = (10 m/s × 12 s) + ​(2 m/ ) d = 120 m + ​(2 m/ ) ) d = 120 m + (288 m) = 120 m + d = 120 m +144 m d = 264 m   Step 2: Find the Distance

10. Solve the following problems: A car starts from rest and accelerates at 3 m/s² for 10 seconds . Find: a) The final velocity of the car b) The distance traveled

11. Solve the following problems: A cyclist moving at 5 m/s accelerates at 2.5 m/s² for 8 seconds while going downhill. Find: a) The final velocity b) The total distance traveled

12. Solve the following problems: A train initially moving at 20 m/s accelerates at 1.5 m/s² for 15 seconds . Find: a) The final velocity b) The total distance traveled

13. 1. A car accelerates from rest at 3 m/s² for 6 seconds . What is the car’s final velocity ? How far does the car travel during this time? Solve the Problem,

14. 2. A cyclist moving at 5 m/s accelerates at 2 m/s² for 4 seconds . What is the cyclist’s final velocity ? How far does the cyclist travel during this time? Solve the Problem,

15. 3. A motorcycle traveling at 20 m/s slows down uniformly at -4 m/s² until it comes to a stop. How long does it take to stop? What is the distance covered before stopping? Solve the Problem,

16. 4. A train accelerates from 8 m/s to 20 m/s in 10 seconds . What is the train’s acceleration? How far does the train travel in this time? Solve the Problem,

17. 5. A ball rolls down a track starting from rest with an acceleration of 1.5 m/s² for 8 seconds . What is the ball’s final velocity? How far does the ball travel in this time? Solve the Problem,

18. 6. A bus traveling at 15 m/s speeds up at 2.5 m/s² for 5 seconds . What is the bus’s final velocity? How far does the bus travel during this time? Solve the Problem,

19. 7. A car accelerates uniformly from 10 m/s to 30 m/s over a distance of 160 meters . What is the acceleration of the car? How long does it take for the car to reach this speed? Solve the Problem,

20. 8. A person running at 6 m/s suddenly stops in 3 seconds with a uniform deceleration. What is the runner’s acceleration? What distance does the runner cover before stopping? Solve the Problem,

21. 9. A skateboarder moving at 12 m/s comes to a stop over a distance of 18 meters . What is the acceleration of the skateboarder? How long does it take for the skateboarder to stop? Solve the Problem,

22. 10. A sports car moving at 25 m/s accelerates at 4 m/s² until it reaches 45 m/s . How long does it take to reach this speed? What is the distance covered during this acceleration? Solve the Problem,

23. Get ¼ sheet of paper ¼ Sir? Yes 1/4

24. Multiple Choice Direction: Choose the correct answer. Write the letter of your choice.

25. 1. A car initially moving at 10 m/s accelerates at 4 m/s² for 5 seconds . What is its final velocity? a) 20 m/s b) 25 m/s c) 30 m/s d) 35 m/s

26. 2. A runner starts from rest and accelerates at 2.5 m/s² for 8 seconds . What is the total distance covered? a) 40 m b) 60 m c) 80 m d) 100 m

27. 3. A train is moving at 15 m/s and accelerates uniformly at 1.8 m/s² for 12 seconds . What is its final velocity? a) 32.6 m/s b) 35.4 m/s c) 37.6 m/s d) 40.5 m/s

28. 4. A stone is dropped from a building and falls freely under gravity ( 9.8 m/s² ) for 7 seconds . How far does it fall? a) 140.7 m b) 170.1 m c) 240.1 m d) 320.4 m

29. 5. A cyclist moving at 5 m/s increases speed with an acceleration of 3 m/s² for 6 seconds . What is its total distance traveled? a) 48 m b) 58 m c) 68 m d) 78 m

30. Correct Answers: b c b b a

31. Assignment: SOLVE THE PROBLEM A cyclist is moving at a constant velocity of 10 m/s for 12 seconds before coming to a stop by applying brakes. Find: a) The total distance traveled before stopping. b) The acceleration if the cyclist takes 4 seconds to stop. A train is moving with an initial velocity of 15 m/s and accelerates at 2 m/s² for 20 seconds . Find: a) The final velocity of the train. b) The total distance covered during this time. A ball is rolling on a frictionless surface with an initial velocity of 5 m/s . A force is applied, causing it to accelerate at 1.5 m/s² for 6 seconds . Find: a) The final velocity of the ball. b) The total displacement during this time .​​