One-Dimensional Kinematics

Goal of the class To understand the basic concepts of kinematics such as average velocity and acceleration To be able to calculate unknown quantities using the SUVAT equations Question of the day: What information can be extracted from a velocity-time graph?

One-dimensional motion In physics we learn the basic equations we usually restrict movement to one dimension e.g. a train moving along its tracks. Varies in x,y or z only Later we will break this restraint and deal with more complex problems.

Relative Motion The speed of an object is often compared to a fixed point. Example: A person walking could be moving at 2 m/s faster than a fixed object. A moving reference point carrying objects will move at the same speed as the reference point

Trains at the Station Have you ever been on a train and you’re not sure whether your train is moving or the other train?

Relative Motion If two trains were traveling next to each other at the same speed, the train would be appear to be still to a passenger on the train A train going in the opposite direction would appear to travel very quickly

At rest When an object is at rest, no motion occurs in the reference frame. The position of the object doesn’t change Some reference frames makes problems easier than others.

Displacement Displacement is the change in the position Has dimensions of length (usually m, km) Displacement = change in position = final position – initial position (delta) = change in

Displacement / Distance vector scalar 0m 60m 30m

Velocity Knowing starting and final position doesn’t describe all of the motion. We need the time too. Average velocity = change in position change in time

Practice problems A man is floating on a raft on a stream with a velocity of 1.8ms-1 East. If he floats for 6 mins, how far has he travelled? (calculate displacement) Sean drives at an average velocity of 56km/hr North for 120km. How long was his journey? If he returns home in 90mins, what was his average velocity for the return trip? (becareful of the sign)

Velocity / speed Most people use speed and velocity in everyday speak but they are different. Average speed is the distance covered in a certain time, where velocity is the displacement covered in the same time. This means for a round trip (ending where you started) your average velocity will always be 0ms-1 when you speed will not be.

Displacement-time graphs Time is always plotted on the x axis Displacement is always plotted on the y axis How fast is the object in this graph moving?

Displacement-time graphs The object is not moving, velocity = 0 m/s Time (s) Displacement (m) 50 5 10 15 20 25 30 35 40 45 55 60

Displacement-time graphs On this graph the displacement changes over time.

Finding the velocity The slope (gradient) of a graph tells you how fast one variable changes in relation to the other In a displacement-time graph the slope is the velocity To calculate the slope of a line you can use this simple formula:

Finding the velocity =120m – 20m =100m =60s – 10s =50s

Velocity What is the velocity between a) 0-15s b) 15-40s c) 40-60s

Velocity How does the velocity behave for the four different systems?

Acceleration Average acceleration is the rate of change of velocity

Acceleration Example: A bus slows down with an average acceleration of -2ms-2. If it takes 4.5s to come to a stop, what was the initial velocity? He accelerates quickly from a velocity of 7ms-1 to 12ms-1. If this is done over 10s, what is the average acceleration?

Acceleration If Δv is positive so is a (A,B) If Δv is zero so is a (C) If Δv is negative so is a (D,E)

Motion with constant acceleration Displacement = area under the graph Acceleration = gradient of the graph

Motion with constant acceleration

Practice A boy pushes a shopping trolley through a supermarket. If he starts from rest and his final velocity is 6m/s. How far does he push it in 10s?

Practice A driver is travelling at 21.8ms-1 east and sees a cat in the road 100m away. How long does it take him to stop in exactly 99m if he decelerates uniformly?

SUVAT notation In a lot of books you will see these equations using the following symbols: s = displacement u = initial velocity v = final velocity a = acceleration t = time

Homework Set #3 Answer questions 6, 14, 20, 38, 44, 58, page 48 on Read the sections if you need help Challenging problem 120

Questions