# Kinematics

**AS level**

- Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration
- Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph
- Understand, use and derive the formulae for constant acceleration for motion in a straight line
- Use calculus in kinematics for motion in a straight line

**A level**

- Use calculus in kinematics for motion in 2 dimensions using vectors
- Model motion under gravity in a vertical plane using vectors; projectiles

### Forces in 1 dimension

This interactive simulation displays graphs for displacement, velocity and acceleration against time graphs under conditions of constant acceleration. All three graphs can be seen simultaneously or individually.

### Runaway Train

In this activity from the Nuffield Foundation, students carry out an experiment to collect data about a trolley rolling down a slope. They then use this data to simulate the motion of a train by fitting a quadratic curve to their data (time,displacement) using a graphic calculator or spreadsheet.

The slideshow provides an introduction to the activity and highlights the modelling cycle, which is the main emphasis of this resource. Students who undertake the extension work may use kinematics or dynamics to determine the velocity of the trolley and hence the acceleration.

### Exploring Mechanics

This resource, produced by the CIMT, is designed to provide a more realistic view of mechanics and help the teaching of mechanics move towards applications and away from straight algebraic manipulation.

The first 5 investigations in "Student Material 2" are short investigations involving constant velocity or constant acceleration in 1 dimension. "Student Material 4: mechanics hints and nudges" provide a more structured route through the investigations. The separate "Teacher Material" provides solutions to the problems.

### Exploring Equations of Motion 02

In this resource, from the Department for Education Standards Unit, students use a past paper examination question requiring them to use the equations of motion for constant acceleration.

The task is intended to become a group activity to allow students to develop their ability to generalise from specific situations of motion.

### Motivating A-Level Mathematics

This resource is a text book produced by the Spode Group covering many topics including Mechanics.

Pages 91-97 of the pdf contain a case study of a car braking, dealing with thinking and braking time. The solution involves equations of motion for constant acceleration formula and constant velocity. Calculus forms part of the case study as simple integration of dv/dt is used to find a function for the velocity.

### Model the Motion

In this activity from the Nuffield Foundation, students match descriptions of a variety of real scenarios involving motion with the corresponding velocity–time and displacement–time graphs.

The resource has a set of teacher's notes and a PowerPoint which can be used to introduce the activity.

While completing this task students will need to consider how realistic or unrealistic the graphs are.

### Constant acceleration equations

This pdf contains worked examples of applying constant acceleration formulae. It also has an exercise of 6 questions with answers.

### Distance-time and Velocity-time Graphs

This resource involves a card sort linking graphs, units and statements relating to distance, velocity, acceleration and time. There are teacher's notes and a suggested lesson plan.

The activity takes students through a step-by-step approach to understanding the basic principles of distance-time and velocity-time graphs. Working through the activity will help students to:

* Understand the terms distance, time, velocity and acceleration

* Interpret different representations of motion

* Translate between word expressions, algebraic expressions, and graphical representations of motion

* Calculate distance, time, velocity and acceleration from given variables or from graphical representations

### The Equations for Uniform Acceleration

This is a link to High School Physics Lab. The equations of motion for constant acceleration are derived using u and v as the inital and final velocity.