Lecture 3 - Day 2 Motion and Kinematics - Acceleration - Complete Motion Diagrams and Turning Points

Oct 25, 2026

Lecture 3, Day 2 focuses on acceleration as the quantity that changes an initial velocity into a final velocity, using vector-based motion diagrams. The session derives relationships between velocity and acceleration and applies them to examples such as a spacecraft landing on Mars, a car speeding up, and motion at constant speed along a curved path. It emphasizes direction-changing acceleration at turning points and introduces how velocity, position, and acceleration graphs connect through slopes and areas.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

Acceleration

Velocity-to-velocity change (motion diagrams)

Direction vs magnitude in constant-speed motion

Turning points and nonzero acceleration

Practice examples and quiz

Cart-pulley motion diagram with vectors

Position, velocity, and acceleration graphs

Lecture 3 / Day 2 Motion and Kinematics Acceleration Complete Motion Diagrams Turning Points So we finished with an example talking about velocity and how velocity is what changes an initial position to a final position. But what changes an initial velocity to a final velocity? Acceleration is what changes an initial velocity to a final velocity. The definition of velocity is: a = ""vt \# "v = a" t v f = vi + a" t or vf = vi + "v Since we know how to add and subtract vectors , let’s do an example of a motion diagram and find acceleration. Example: A spacecraft lands on Mars with a parachute. Draw a motion diagram to describe the motion. vi Δv Δv Δv vf Δv So we can see that the spacecraft is slowing down and that our acceleration vectors are pointing in the direction opposite to the velocity. Let’s do a few simple examples of a car on a track: Draw the velocity and acceleration vectors for the car speeding up: a a a Notice for the car speeding up the acceleration points in the same direction as the velocity. Now try the car going around a curve at constant velocity: Notice that going around a curve at constant velocity there is an acceleration. But by definition , a = "tv , if vi = vf , Δv = 0 so a = 0. This would imply that going around a curve at constant velocity , acceleration should be zero! So why is a≠0? Think about this while trying your own diagram: a car going over the opposite curve at constant velocity. So let’s answer the question , how can you have an acceleration at constant velocity? The truth is , the magnitude is constant , but the direction is changing. So there has to be an acceleration if the velocity is changing direction , because acceleration is what changes an initial velocity to a final velocity. Also notice that the acceleration points to a common point , the center of the circle. It makes sense if you think about it , to keep something going in a circle you have to have an acceleration toward the center. Think of a ball on a string , which you swing around. If you cut the string the ball will go off in a new direction – no longer in a circle. The string is what provides that acceleration to keep it in a circle. Now we’ll have you do some examples: • A car rolls down a hill after the parking brake fails • Bob runs once around a track with straight sides and semicircular ends • A ferris wheel goes around once at constant speed a a = 0 a = 0 No acceleration on the straight bits , but notice that acceleration points to the center of the semi-circles. Acceleration for the ferris wheel should point toward the center. Even though the speed of the ferris wheel doesn’t change , there is an acceleration because the direction of the velocity is changing. So now let’s try a quick quiz question. A car drives over a hill at a steady 60 mph. Is it accelerating as it crosses the crest of a hill? Justify your answer using a complete motion diagram Now let’s consider a new type of situation: [cart attached to mass over pulley , push against force of mass and allow to return] Now let’s do a motion diagram including velocity and acceleration vectors. a a a a a a Notice something very important , the object slows down when acceleration is opposite velocity , and the object speeds up when acceleration is in the same direction as velocity. What about the turning point , what’s the acceleration there? We’ll split the class into two groups , since there are two possibilities: a = 0 , a≠0 each has to choose a spokesman and defend the position. Ultimately , acceleration at the turning point cannot be zero by the definition of acceleration – acceleration is what changes initial velocity to final velocity. If we look at the vectors: -vi vf Δv Δv is definitely not equal to zero. In fact it is pretty big compared to the other acceleration vectors. This is because you have to go from velocity to the left to a change that gives you velocity

FAQs

How does acceleration relate to changing velocity?

Acceleration is what changes an initial velocity into a final velocity. When acceleration is opposite the velocity, the object slows down; when aligned with velocity, it speeds up.

Why can acceleration exist even when speed is constant on a curve?

Because the velocity direction changes. Even if the magnitude stays constant, the change in velocity direction means acceleration is nonzero and points toward the center of the circular path.

What is the acceleration at a turning point?

At the turning point, acceleration cannot be zero by the definition of acceleration as the change from an initial velocity to a final velocity. The motion diagram vectors show a significant change in velocity direction.

Oct 25, 2026

Uploaded by River Wang