1. Equations involving Constant Acceleration & Working with Kinematics Graphs Physics 11

2. Kinematics Equations for Constant Acceleration

3. Sample Problem If a rocket with an initial velocity of 8.0 m/s at t = 0 s accelerates at a rate of 10.0 m/s 2 for 2.0 s, what is its final velocity at t = 2.0 s ?

4. Kinematics Equations for Constant Acceleration

5. Sample Problem What is the displacement of a bullet train as it is accelerated uniformly from +15 m/s to +35 m/s in a 25 s time interval?

6. Kinematics Equations for Constant Acceleration N.B.: If an object starts from rest, then v i = 0 m/s and d = ½ at 2 (i.e. this d-t graph looks like a parabola)

7. Sample Problem A car starting from rest accelerates uniformly at +7.2 m/s for 8.0 s. How far does the car move?

8. Kinematics Equations for Constant Acceleration Note: this equation does not involve time !

9. Sample Problem An airplane must reach 75 m/s for take-off. If the runway is 0.5 km long, what must the constant acceleration be?

10. Acceleration due to Gravity "g" is a vector quantity -g= -9.81 m/s 2 (an average value across Earth) N.B.: neglect air resistance g can be substituted in equations for constant acceleration previously in notes

11. Sample Problem A 3.0-kg stone is dropped for a height of 5.0 m. How long does it take to reach the ground? What is its velocity at the moment it hits the ground?

13. From Position-Time to Velocity-Time to Acceleration-Time We have seen that we can use slopes (whether from constant or instantaneous velocity) from a position-time graph to find information to draw a velocity-time graph Further, we have seen that using slopes from a velocity-time graph will provide information to draw an acceleration-time graph

14. From Acceleration-Time to Position-Time A car accelerates at a constant 0.75m/s 2 ; plot an acceleration-time graph to represent this situation (showing time to 10 seconds) On the graph, calculate the area under the curve for the following times:  0s-2.5s  0s-5s  0s-7.5s  0-s-10s What are the units of the area? What does this mean?

15. From Acceleration-Time to Position-Time

16. Use the velocity data from the previous question (area under the curve) to plot a velocity time graph. From the velocity time graph, calculate the area under the curve for the following time intervals:  0s-2.5s  0s-5s  0s-7.5s  0s-10s What are the units of the area? What does this mean?

17. From Acceleration-Time to Position-Time

18. Use the displacement information from the previous question (area under the curve) plot a displacement–time graph

19. From Acceleration-Time to Position-Time

20. Acceleration-Time Graph

21. Velocity-Time Graph

22. Position-Time Graph

23. Equations of Motion