Acceleration

Acceleration measures the rate of change of velocity during a given time interval a = Δv Δt Therefore, the units of m/s or m/s2 s Acceleration has a magnitude and a direction, so it is a vector quantity

Formula for Average Acceleration is: Use this equation when you are given acceleration, velocity, and/or time BUT there is NO MENTION of a displacement!

Ex: As a shuttle bus comes to a stop, it slows from 9. 0 m/s to 0 Ex: As a shuttle bus comes to a stop, it slows from 9.0 m/s to 0.0 m/s in 5 s. Find the acceleration of the bus. a = Δv/Δt a = vf – vi/Δt a = 0.00 – 9.00/5 a = -1.8 m/s2

You can rearrange the previous equation to solve for an unknown variable; this is how you would rearrange the formula to solve for the final velocity:

Ex: A bus that is traveling at 8 Ex: A bus that is traveling at 8.33 m/s speeds up at a constant rate of 3.5 m/s2. What velocity does it reach 6.8 s later? a = Δv/Δt rearranged to: a(Δt) + vi = vf 3.5(6.8) + 8.33 = vf 23.8 + 8.33 = vf 32 m/s = vf

Another Acceleration Equation: xf = xi + vit + ½at2 Use this equation when you are given acceleration, initial velocity, displacement, and/or time!

Ex: An airplane, initially moving at 3 Ex: An airplane, initially moving at 3.0 m/s down a runway, begins to accelerate down the runway at 3.6 m/s2. How far down the runway will it be in 20 s?

How to solve… List out all known and unknown variables vi = 3.0 m/s a = 3.6 m/s2 Δt = 20 s xf = ? Hint: unless otherwise stated, we assume that the initial location (xi) is always 0

2. If you do not need to rearrange the equation, then plug the variables into the formula. xf = xi + vit + ½at2 xf = 0 + 3.0(20) + ½(3.6)(20)2 xf = 0 + 3.0(20) + ½(3.6)(400) xf = 0 + 60 + 720 xf = 780 m

Last Acceleration Equation: vf2 = vi2 + 2aΔx Use this equation when you are given acceleration, velocity, and/or displacement BUT there is NO MENTION of time!

Ex: A babysitter pushing a stroller starts from rest and accelerates at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?

How to solve… List out all known and unknown variables vi = 0 m/s (starts from rest) a = 0.500 m/s2 vf = ? Δx = 4.75 m

2. If you do not need to rearrange the equation, then plug the variables into the formula. vf2 = vi2 + 2aΔx vf2 = 02 + 2(0.500)(4.75) vf2 = 4.75 √vf2 = √4.75 vf = 2.2 m/s

There may be acceleration problems where we calculate the movement of objects in free fall Neglecting air resistance, all freely falling objects (dropped or thrown), fall at the same rate of acceleration i.e., the rate of gravity The variable for gravity is g g = -9.80 m/s2 *Notice the units of gravity…this should remind you that gravity is a specific acceleration*

Ex: A stone falls freely from rest for 8. 0 s Ex: A stone falls freely from rest for 8.0 s. What is the stone’s velocity after 8.0 s?

2. Given the above info, the formula to use is: a = Δv/Δt 1. We know: vi = 0 m/s vf = ? t = 8.0 s a = -9.8 m/s2 2. Given the above info, the formula to use is: a = Δv/Δt *Note: I chose this formula b/c it was the only one without a displacement*

*Note: negative velocity accounts for direction of motion (downwards) I rearranged the formula to solve for the final velocity: vf = a(Δt) + vi vf = a(Δt) + vi vf = -9.8(8.0) + 0 vf = -78.4 m/s *Note: negative velocity accounts for direction of motion (downwards)

Acceleration Graphs: Velocity vs. Time

Acceleration Graphs: Velocity vs. Time

What’s going on during each segment?