Episode 205: Describing motion

This episode introduces (or revises) basic kinematics. The equations of motion are met in separate science (triple award) pre-16 level but are not discussed in detail in double award. This is an area which many moderate-to-weak students find difficult and they may well remember their pre-16 experience with some unease. It is worthwhile including a direct measurement activity to ensure that students spend sufficient time on the basic physics of velocity, distance and time. This is a busy episode that focuses on one activity that all students should perform individually.

Summary

  • Discussion: Scalars and vectors, velocity and displacement (5 minutes)
  • Student experiment: Balls down ramps (25 minutes)
  • Discussion: Average velocity, time and displacement (10 minutes)
  • Discussion: Chalk in the air (5 minutes)
  • Student questions: Using these ideas (30 minutes)

Discussion: Scalars and vectors, velocity and displacement
If necessary, briefly remind students of the difference between vectors and scalars. Taking a marble and rolling it along the bench in one direction then back along the bench in the other direction at the same speed clearly demonstrates the difference between velocity and speed. Defining acceleration as the rate of change of velocity allows a discussion of an orbiting body (or a conker on a string) moving with constant speed whilst also experiencing constant acceleration.

Before proceeding with the student experiment it is worthwhile explaining why the final velocity of a body is twice its average velocity if (and only if) it has uniformly accelerated from rest.

Experiment with the marble rolling down a ramp

Student experiment: Balls down ramps
Rolling balls down ramps: This is a version of the experiment that Galileo performed towards the end of the sixteenth century. Students time a marble rolling a fixed distance down the slope. From this, they can produce graphs of final velocity against distance and final velocity against time. The first graph will show a square relationship whereas the velocity-time graph will show a linear relationship. However, there is much scatter in the points and it is a useful exercise to consider whether the velocities are more ‘accurate’ for readings over small distances than those over larger distances.

Episode 205-1: Rolling balls down ramps (Word, 39 KB)

Discussion:Average velocity, time and displacement
Using the graphs drawn from the experiment you can show two things:

a = Dv/Dt, that is, that the gradient of a velocity-time graph yields acceleration.

The area under the velocity time graph gives the distance travelled by the marble.

Ask your students to read off a time (say 1.5 s) from the distance-time graph and find the corresponding distance value. The area under the velocity-time graph up to 1.5 s will come to the same value as the distance. Bright students will see the circularity in this method, but this, in itself, is of value.

Discussion: Chalk in the air
Throw a piece of chalk (or a board marker) in the air vertically and catch it when it returns to its original position. Ask students to sketch a velocity-time graph of the motion, assuming no air resistance.

Very few will produce a graph like this:

Velocity - time graph

The errors made by the students will allow you to highlight many points of physics. For instance, a graph may suggest that the acceleration due to gravity is different when a body is travelling upwards from the value for a descending body. Particularly revealing is to ask what is the acceleration when the object reaches its maximum height. You will find this a fruitful discussion from which even the bright and confident students can learn a lot.

Student questions: Using these ideas
Select from the questions those most suitable to the level of your students. You might choose to give different questions to different students – for example, those not taking post-16 level mathematics might need to work through more examples than those studying mathematics.

Episode 205-2: Distance, time and speed calculations (Word, 63 KB)

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Episode 205: Describing motion (Word, 106 KB)