P3b(i) Changing Speed You will learn about: How to analyse speed-time graphs Use the speed-time graph to calculate acceleration Use the speed-time graph to work out the distance travelled

Speed-Time graphs Speed-Time graphs look similar to Distance-Time graphs but they are NOT THE SAME These three graphs represent the motion of a car in three situations. This graph shows that during the time period the speed is the same. Therefore the car is moving at a constant speed (5m/s in this case). A plateau = constant speed This graph shows that during the time period the speed is increasing and increasing. Therefore if the speed is constantly increasing then the car must be accelerating. The line is positive so this is positive acceleration. An incline = positive acceleration This graph shows that during the time period the speed decreasing and decreasing. Therefore if the speed is constantly decreasing then the car must be decelerating. The line is negative so this is negative acceleration. A decline = negative acceleration

Speed-Time Graph Gradients Both of these lines are moving downward – they each show negative acceleration – they are each slowing down. The blue line has a steeper gradient. It therefore has a bigger negative acceleration – it slows down more rapidly than the red line. The steeper the gradient: The more rapidly it accelerates (negative OR positive)

More about gradients Both these lines show positive acceleration. The red line is accelerating more rapidly. The red line also covers a greater distance therefore the car travels further. The AREA under the red line is greater. Steeper gradient = More rapid acceleration; More distance covered.

Calculating Distance from a Speed- Time Graph To calculate the distance you need to use this equation: Distance travelled = area under speed-time graph The area of a triangle can be calculated using: ½ x base x height So during the journey shown in the graph we can calculate the distance by working out the area under the line. The base measures 10 The height measures 20 Therefore: ½ x 10 x 20 = 100m

Using Speed-Time Graphs to calculate Acceleration Here the gradient = 20/10 = 2m/s 2 Notice that the unit for acceleration is m/s 2 whereas for speed the unit is just m/s. This m/s 2 means that the speed increases and increases which is what acceleration is.

Trickier acceleration calculations This line does not cross the x-axis so to calculate the area beneath the line we need to add together the areas of a triangle AND a rectangle. 0 Area of Triangle = ½ x base x height = ½ x 10 x 20 = 100m Height = 26-6 = 20 Base = 10 – 0 = 10 Area of Rectangle = base x height = 10 x 6 = 60m Height = 6 – 0 = 6 Now add the amounts: Area of Triangle + Area of Rectangle = 100m + 60m = 160m

Estimating distance from a Speed-Time graph In this graph we cannot draw exact triangles or rectangles to calculate the distance travelled. But we can estimate it by drawing rough shapes: One triangle has an area = ½ x b x h = ½ 3.5 x 15 = m There are two triangles so = 2 x = 52.5m The rectangle has an area = b x h = 3 x 20 = 60m Add together the areas of the two triangles and rectangle = 52.5m + 60m = 112.5m REMEMBER: The shapes do not exactly fit under the curve so this is just an approximation.

Questions 1.A lorry brakes really hard. What would it look like on a speed-time graph? 2.Two dogs race one another. One wins and one loses. Which variable was the same for both of them? 3.An aeroplane accelerates uniformly from rest reaching a speed of 1,500 m/s in 60 seconds. How far did it travel? 4.What would the speed-time graph look like for a car driving round a roundabout at 30 miles/h?

Questions 1.A lorry brakes really hard. What would it look like on a speed-time graph? A negative sharp gradient – reaching the x-axis when it stopped 2.Two dogs race one another. One wins and one loses. Which variable was the same for both of them? Distance travelled 3.An aeroplane accelerates uniformly from rest reaching a speed of 1,500 m/s in 60 seconds. How far did it travel? Using area under line equation = ½ x b x h = ½ x 60 x 1500 = 45,000m 4.What would the speed-time graph look like for a car driving round a roundabout at 30 miles/h? A plateau in line with 30 miles/h on the y-axis