1. STARTER Rearrange the equation for acceleration, solving for v f = v. Rearrange the equation for acceleration, solving for v f = v. Start with a = (v - u )/t and solve for v. v = u + at

2. Kinematic Equations for Constant Acceleration If the acceleration is constant, a =  v/  t = (v - u )/t or 1. v = u + at

3. If a = constant, v vs. t is a straight line. The average value of v is halfway on the line, so: Vavg = ½(u +v) = s/t,or s = (t/ 2 )(u +v)

4. So far: 1. v = u + at 2.s = (t/2)(u +v) Solving 1. for t and inserting into 2 gives you : s = ((v -u)/2a)(v +u) Or v 2 = u 2 +2as

5. So far: 1. v = u + at 2. s = (t/2)(u +v) Substituting 1. into 2. gives: s = (t/2)(u +u +at), or s = ut + 1/2 at 2 3. v 2 = u 2 +2as

6. Finally, the Four Kinematic Equations 1. v = u + at 2. s = (t/2)(u +v) 3. v 2 = u 2 +2as 4. s = ut + ( 1/2) at 2

7. How To Use Them 1 st List the possible unknowns s = v = a = u = t = 2 nd Read the problem and fill in all you can. 3 rd Choose a kinematic equation with just one unknown in it.

8. 1 st List the possible unknowns – fill in. Example A car starts from rest and accelerates to 40 m/s in 10 seconds. 1.What is the acceleration of the car? 2. How far does the car move? s = v = a = u = t = s = ? v = 40 a = ? u = 0 t = 10

9. To get a, you need an equation with a in it, but without s. Which one is it? v = u + at 40 = 0 + 10a or a = 4.00 m/s 2 s = ? v = 40 a = ? u = 0 t = 10

10. To get s you have a choice. Using 2., s = (t/2)(u +v) s = (10/2)(0 +40) = 5(40) = 200m s = ? v = 40 a = ? u = 0 t = 10

11. Example A car moving at 50m/s sees a dog in the road 100m ahead. If the drivers stops just in time, what acceleration must the brakes provide? How long does it take to stop? 1.What is the acceleration of the car? 2.What is t? s = v = a = u = t = s= 100 v = 0 a = ? u = 50 t = ?

12. To get a, you need an equation with a in it, but without t. Which one is it? v 2 = u 2 + 2 as 0 =50 2 + 200a or a = -50 2 / 200 = -12.5 m/s 2

13. To get t, you have a choice. Let’s use: v = u + at 0 =50 -12.5t or t = -50 /-12.5 = 4.00 seconds s= 100 v = 0 a = ? u = 50 t = ?

14. Summary 1. v = u + at 2. s = (t/2)(u +v) 3. v 2 = u 2 +2as 4. s = ut + ( 1/2) at 2

15. EXIT A relay runner moving at 2 m/s, speeds up to 6m/s in 4 seconds. What is her acceleration?