1. 1 PPMF101 – Lecture 4 Motions in 1 & 2 Dimensions

2. 2 Vector & Scalar quantity Vector A quantity that has magnitude and direction. Eg. Displacement, velocity, acceleration, force, momentum, impulse, weight, friction, tension, electric and magnetic field. Scalar A quantity that has magnitude only. Eg. Distance, speed, pressure, energy, heat, work, power, time, charge and temperature.

3. 3 Distance & Displacement Distance Scalar quantity Magnitude only Displacement Vector quantity Magnitude and direction

4. 4 Speed Speed refers to how far an object travels in a given time interval, regardless of direction. A scalar quantity.

5. 5 velocity Velocity is used to signify both the magnitude (numerical value) of how fast an object is moving and the direction in which it is moving. A vector quantity.

6. 6 Instantaneous velocity Instanteneous velocity at any moment is defined as the average velocity over an infinitesimally short time interval.

7. 7 Acceleration Acceleration specifies how rapidly the velocity of an object is changing. If velocity is increasing it is called acceleration. If velocity is decreasing it is called negative acceleration or deceleration.

8. 8 Instantaneous acceleration

9. 9 Graph: displacement (s) vs time (t) Slope = velocity s t s t constant velocity zero velocity

10. Graph: displacement (s) vs time (t) 10 s t increasing velocity s t decreasing velocity

11. 11 Graph: velocity(v) vs time(t) (p.25) Slope = acceleration Area under the graph = distance travelled v t velocity increasing uniformly & constant acceleration v t constant velocity & zero acceleration

12. 12 Graph: acceleration(a) vs time(t) For constant acceleration. The graph is a straight horizontal line.

13. 13 v vs t & s vs t graphs: braking distances

14. 14 S vs t & v vs t graphs: catching a speeder (p.31)

15. 15 Equations of motion Constant acceleration a Constant acceleration due to gravity g

16. Examples 1. A runner leaves the starting blocks and accelerates at 2.50 m/s2 for 4.00 s. What speed does the runner reach? 2. An airplane that is flying level needs to accelerate from a speed of 200 m/s to a speed of 240 m/s while it flies a distance of 1200 m. What must the acceleration of the plane be? 16

17. 3. A rock is dropped from a vertical cliff. The rock takes 7.00 s to reach the ground below the cliff. What is the height of the cliff? 4. If an object was freely falling, from what height would it need to be dropped to reach a speed of 70.0 m/s before reaching the ground? 17

18. 18 Eg. 1 Determine the average velocity for (i) the first 3 seconds (ii) the entire motion

19. 19 Eg. 2 This is a graph for a moving object.

20. 20 Eg. 2 continue (i) Explain the motion at PQ and RS. (ii) What is the total displacement of the object? (iii) What is the time for the motion of the object? (iv) Determine its average velocity. (v) What is its acceleration at t = 22 s? t = 22 s?

21. 21 Eg. 3 A car is driven from point O at the north with velocity 60 km/h for 10 min until it reached a junction, S. The car then turn west and moved with a velocity of 30 km/h for another 10 min until its reached point A. Determine (a) the average speed of the car from O to A. (b) the average velocity of the car from O to A.

22. 22 Eg. 4 A mouse deer runs a distance of 70 m between two points at a constant acceleration in 7.0 s. Its velocity while passing through the second point is 15.0 m/s. (a) What is its speed at the first point? (b) What is the acceleration of the mouse deer?

23. Projectile Motion A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola. 23

24. Projectile Motion If an object is launched at an initial angle of θ 0 with the horizontal, the analysis is similar if θ 0 = 0 launched from certain height, except that the initial velocity has a vertical component. 24

25. It can be understood by analyzing the horizontal and vertical motions separately. Projectile Motion 25

26. Projectile Motion The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration g. This photograph shows two balls that start to fall at the same time. The one on the right has an initial speed in the x-direction. It can be seen that vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly. 26

27. Projectile Motion Projectile motion is motion with constant acceleration in two dimensions, where the acceleration is g and is downward. 27

28. Solving Problems Involving Projectile Motion Example 3-6: Driving off a cliff. A movie stunt driver on a motorcycle speeds horizontally off a 50.0-m-high cliff. How fast must the motorcycle leave the cliff top to land on level ground below, 90.0 m from the base of the cliff where the cameras are? Ignore air resistance. 28

29. Projectile Motion Examples of projectile motion. Notice the effects of air resistance. 29 Water fountainfireworks metal grinding