1. Advanced Higher Physics Unit 1 Kinematics relationships and relativistic motion

2. Kinematic relationships Kinematics is the study of motion without reference to cause. From Higher Physics, we know: We now need to prove this equations using calculus.

3. Velocity Average Velocity is defined as the change in displacement (Δs) over time (Δt). Instantaneous velocity is defined as the speed at any particular time during a journey. This velocity can be found by measuring the average velocity over a very short time interval. (as Δt →0)

4. Acceleration Acceleration is defined as the change in velocity (Δv) over time (Δt). Instantaneous acceleration is defined as the acceleration at any particular time during a journey. This acceleration can be found by measuring the acceleration over a very short time interval. (as Δt →0)

5. If then (This formula can be found in the data booklet)

6. v = u + at at t=0, v = u, c=u integrate

7. s = ut +½at² at t=0, s=0, c=0 integrate

8. v²=u²+2as taking a common factor of 2a gives and since s = ut + ½at 2

9. A very useful extra equation is Displacement-time and velocity-time graphs can be used to derive information.

10. Example Q1a) 2007 1.(a)A particle has displacement s = 0 at time t = 0 and moves with a constant acceleration a. The velocity of the object is given by the equation v = u + at, where the symbols have their usual meanings. Using calculus, derive an equation for the displacement s of the object as a function of time t.

11. Answers at t=0, s=0, c=0 integrate

12. Relativity The greatest possible speed is the speed of light in a vacuum: At very high velocities an object appears to have gained mass to the viewpoint of a stationary observer. The mass gain can be calculated using: Available on DATA SHEET Rest mass (kg) speed of object (ms ˉ ¹) speed of light in a vacuum (ms ˉ ¹) Available in DATA BOOKLET Object mass (kg) The rest mass of an object is its mass when it is stationary.

13. Relativistic energy The total energy of an object is: speed of light (3x10 8 ms -1 ) relativistic mass (kg) relativistic energy (J) This energy is made of two parts: Kinetic energy of motion rest mass energy relativistic energy Relativistic effects are only taken into account when v>10%c. in DATA BOOKLET Not in DATA BOOKLET

14. Example Q1. (b) 2007 A proton is accelerated to a high speed so that its mass is 2.8 times its rest mass. 1.Calculate the speed of the proton. 2.Calculate the relativistic energy of a proton at this velocity.

15. Answers 1.Find the speed using:Rearrange

16. The relativistic energy is given by: