In this section you will: Determine mathematical equations for finding the following based on constant acceleration. Section 3.2-1

Final Velocity from time and acceleration If an object’s average acceleration during a time interval is known, then it can be used to find the change in velocity. The definition of average acceleration: can be rewritten as follows: Section 3.2-2

Final Velocity from time and acceleration The equation for final velocity with average acceleration can be written as: This gives an equation for finding final velocity if initial velocity, avg acceleration and time are known. Section 3.2-3

Displacement From constant Velocity If you know the velocity and time moved you can determine the displacement for the object moving. Section 3.2-8

Displacement with acceleration Average velocity = (vf + vi)/2 Because of this… d=(vf + vi)/2 x t

df = di + vit + 1/2at2 from Displacement with acceleration v = ½(v + v0)   v = ½ [(v0 + aΔt) + v0]  v = ½(2v0 + aΔt)  v = v0 + ½aΔt

Displacement with acceleration Rearrange the equation vf = vi + ātf, to solve for time: Section 3.2-26

Final Velocity without Time This equation can be solved for the velocity, vf, at any time, tf. Section 3.2-27

Equation Review- IMORTANT!!! 4 Kinematic Equations Bases on Constant Acceleration 1- d = (vf + vi)/2*t, Variables- vf, vi, t and d (often vf or vi = 0) 2- vf= vi + at, Variables- vf, vi, a (often vf or vi = 0) 3- df= di + vit + ½ at2, Variable- df, di, vi, t, a (often df, di or vi = 0) 4- vf2 = vi2 + 2a∆d, Variables- vf, vi, a, ∆d (often vf or vi = 0) Section 3.2-25

Question 1 A position-time graph of a bike moving with constant acceleration is shown below. Which statement is correct regarding the displacement of the bike? Section 3.2-28

Question 1 A. The displacement in equal time intervals is constant. B. The displacement in equal time intervals progressively increases. C. The displacement in equal time intervals progressively decreases. D. The displacement in equal time intervals first increases, then after reaching a particular point, it decreases. Section 3.2-29

Answer 1 Reason: You will see that the slope gets steeper as time progresses, which means that the displacement in equal time intervals progressively gets larger and larger. Section 3.2-30

Question 2 A car is moving with an initial velocity of vi m/s. After reaching a highway, it moves with a constant acceleration of a m/s2, what will be the velocity (vf) of the car after traveling for t seconds? A. vf = vi + at B. vf = vi + 2at C. vf2 = vi2 + 2at D. vf = vi – at Section 3.2-31

Answer 2 Reason: Since a = Δv/Δt vf - vi = a (tf - ti) Also since the car is starting from rest, ti = 0 Therefore vf = vi + at (where t is the total time) Section 3.2-32