Chapter 7: Graphs of Motion

7.1 Distance-Time Graphs

• A distance-time graph: vertical axis = distance; horizontal axis = time; gradient = rate of change in distance = speed. (p.184)
• Speed = Distance / Time. (p.184)
• To draw from a table: choose suitable scales, plot the (time, distance) points, then join them with a ruler. (p.185)
• To draw from an equation (e.g. s = 80t): build a table of values, plot and join; two points are enough for a straight line. (p.185)
• Gradient = vertical distance / horizontal distance. (p.187)
• Positive gradient: motion at uniform speed; zero gradient: no change in distance, i.e. stationary; negative gradient: object moves back to its original place or in the opposite direction. (p.187)
• A negative sign for speed only shows opposite direction of motion; speed is stated as a positive value. (p.188)
• km h⁻¹ can also be written km/h. (p.188)
• Average speed = Total distance / Total time. (p.189)
• Distance = Speed × Time; Time = Distance / Speed; 1 minute = 1/60 hour. (p.189)
• Where speed is not given directly, use two points on a straight section of the graph (the gradient is the same along a straight line). (p.188)
• Problem solving: equal gradients (rates of change) give equations such as (65 − 0)/(52 − 0) = (135 − 65)/(t − 77). (p.192)

7.2 Speed-Time Graphs

• A speed-time graph: vertical axis = speed; horizontal axis = time; gradient = rate of change of speed = acceleration. (p.195)
• To draw from a table or equation (e.g. v = 800 − 1 600t): list values, plot points and join. (p.196)
• The area under a speed-time graph = the distance travelled in that time interval. (p.197)
• Use the same time unit for speed and time when calculating distance (e.g. 6 minutes = 6/60 hour). (p.198)
• Area of a trapezium = ½ × (sum of parallel sides) × height; area of a rectangle = base × height. (p.198)
• Acceleration = Change of speed / Change in time (positive gradient). (p.200)
• Zero gradient: no change of speed, uniform speed; area of the rectangle = distance travelled. (p.200)
• Negative gradient: speed decreases = deceleration (negative acceleration); direction of motion stays the same. (p.200)
• Distance: length of the space between two points. Displacement: vector distance from a fixed point in a certain direction. (p.200)
• Speed = rate of change in distance. Velocity = Displacement / Time (rate of change in displacement). (p.200)
• Deceleration can be stated either as a negative acceleration or as a positive deceleration of the same value. (p.202)
• Problem solving: form equations from areas (distance) and gradients (acceleration), e.g. acceleration = (v − 10)/(14 − 10) = 3.5 → v = 24. (p.203)
• Check answers by recalculating the distances from the graph. (p.204)