Acceleration

Warm- up Define velocity Give an example (If you have not done so – hand in your lab)

A recap of Motion Motion can be in: Uniform motion A straight line Circle/curved path Back and forth motion Uniform motion The simplest kind of motion Along a straight line Feels smooth No change in velocity

What if motion is not constant? Un-uniform motion Along a curved or up and down path Feels bumpy Ex: roller coasters, stop and go traffic, walk/jog/walk Change in velocity This is acceleration!! The rate* at which an object’s velocity changes *rate = a change over time

Is there a change in velocity? You are riding your bike at 9 km/hr. Ten minutes later, your speed is 6 km/hr You ride your bike around the block at a constant speed of 11 km/hr You ride your bike in a straight line at a constant speed of 10 km/hr You are stopped at a red light and then it turns green

Three types of Acceleration Positive acceleration Negative acceleration Change in direction

Speeding up & Slowing down Magnitude of the velocity is getting larger when speeding up (+ acceleration) and smaller when slowing down (- acceleration) + Velocity is above the x-axis, - velocity is below the x-axis

Doing the math To find acceleration: A = ∆V ∆ t ∆ is the greek letter delta and means “the change in” To find the change in velocity: final velocity of the object (Vf) minus initial velocity of the object (Vi) To find the change in time: final time of the object’s motion (tf) minus initial time of the object (ti)

What’s the unit? Acceleration is a unit of speed divided by a unit of time Ex: m/s/s Can also be written as m/s2 Ex: km/hr/s Ex: km/hr/hr Can also be written as km/hr2 What does this unit mean? It tells you how much velocity is changing per unit of time Ex: 5 m/s2 Means that velocity is increasing (because it’s a positive #) by 5 m/s every second that the object travels

What does it mean? Ex 2: if a car is accelerating at a rate of 10 m/s/s then its velocity is increasing by 10 m/s every second it is traveling 1s = 10 m/s 2s = 20 m/s 4s = 40 m/s 3s = 30 m/s

Some words to look out for Zero words Words that either mean the objects starts at rest (not in motion) or stops its motion Stop At rest At a standstill

Let’s calculate A jet starts at rest at the end of a runway and reaches a speed of 80 m/s in 20s. What is its acceleration? Write what is given: Vi = 0 m/s (it started at rest) Vf = 80 m/s ∆t = 20 s Solve for acceleration:

Let’s calculate…again A skateboarder is moving in a straight line at a speed of 3 m/s and comes to a stop in 2 seconds. What is his acceleration? Write what is given: Vi = 3 m/s Vf = 0 m/s (came to a stop) ∆t = 2 s Solve for acceleration:

Velocity – Time Graphs Velocity-Time graphs show the change of velocity over an elapsed time AKA Speed-Time graphs Remember that speed does NOT take into account direction Time is always the independent variable Velocity is always the dependent variable

The slope of a Velocity-Time graph is equal to acceleration Slope = rise/run Slope = change in velocity / time a = Δv / t The steeper the slope, the faster the acceleration Remember acceleration can be speeding up, slowing down, or sharp turns A positive slope is speeding up and moving forward A negative slope is EITHER slowing down OR moving backwards A zero slope means that the velocity is NOT changing, meaning that the object is moving at the same speed in the same direction

Check Your Understanding Which person(s) could be slowing down? Person C. They have a negative slope; they could be moving backwards too (there is not enough info on the graph to tell).

Check Your Understanding

Calculating

Helpful hint There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable