Section 1 b) Specification

1.2 plot and interpret distance-time graphs

Distance-time graphs show the change in time on the x-axis (which tells us how long the object took to travel a distance) and the change in distance on the y-axis (which tells us how far an object has travelled from the starting point).
Based on this, the gradient of the lines tells us the average velocity of the object (e.g. a straight horizontal line indicates a stationary object). The steeper the gradient is, the faster the object is travelling. A negative gradient means the object is travelling back closer to the starting point.

1.3 know and use the relationship between average speed, distance moved and
time:
average speed = distance moved / time taken
s = d / t

The relationship shown in this formula is represented clearly by this triangle:

This shows us that we can rearrange the formula to suit the information we have, and the information we wish to obtain.

1.4 describe experiments to investigate the motion of everyday objects such as
toy cars or tennis balls

You could use ticker tape and a toy car on a ramp to plot a distance time graph of its movement. A mark is made on the tape at a regular interval, set by the user (e.g. every second). The distance between marks can be measured and the movement of the car plotted on a distance-time graph.

Another way of investigating the movement of an object, for example a tennis ball, is by dropping it or pushing it down a ramp and measuring the time it takes for the ball to reach a certain point after it begins moving. From this, the average speed can be calculated using the speed triangle.

1.5 know and use the relationship between acceleration, velocity and time:
acceleration = change in velocity/time taken
a = (v-u)/t

Acceleration is the change in velocity divided by the period of time it took for the velocity to change.

By rearranging the equation, we can work out different variables in a situation, depending on the information we have and the information we need, similar to the speed triangle.

1.6 plot and interpret velocity-time graphs

The y-axis shows velocity, and the x-axis shows time. The gradient tells us the acceleration of the object, meaning that a positive gradient is accelerating, a negative gradient is decelerating, and a horizontal line means the object is travelling at a constant velocity. The steeper the gradient, the more quickly the object is increasing or decreasing in velocity. An object that is travelling at a constant speed, then comes to a sudden stop will have a horizontal gradient, followed by a very steep negative gradient.
We can work out the area beneath the line to find the distance travelled. A negative velocity means the object is travelling in a negative direction - the opposite direction (e.g. a car reversing)
(further information on v-t graphs here)

1.7 determine acceleration from the gradient of a velocity-time graph

Acceleration can be determined by calculating the gradient of a v-t graph, and represented with the appropriate units (e.g. if v is in m/s and t is in s, a will be m/s/s or m/s^2)

1.8 determine the distance travelled from the area between a velocity-time
graph and the time axis.

The distance travelled by an object from the starting point can be determined by calculating the area between the x-axis and the lines plotted on the graph.

As represented in the graph above, each of the differently coloured areas can be calculated and then added together to find the distance travelled by the object.
10 x 20 / 2 = 100
20 x 20 = 400
40 x 20 / 2 = 400
= 900 metres