Analysing Motion - Kinematics PDF

Analysing motion Distance-time graphs A distance-time graph shows how far something travels over a period of time. The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start. Features of the graphs When an object is stationar...

Analysing motion Distance-time graphs A distance-time graph shows how far something travels over a period of time. The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start. Features of the graphs When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed in a straight line, the line on the graph is straight but sloped. Note that the steeper the line, the faster the object is travelling. The purple line is steeper than the green line because the purple line represents an object which is moving more quickly. Acceleration You can calculate the acceleration of an object from its change in velocity and the time taken. Velocity is not exactly the same as speed. Velocity has a direction as well as a speed. For example, 15 m/s is a speed, but 15 m/s North is a velocity (North is the direction). Commonly velocities are + (which means forwards) or - (which means backwards). For example, -15 m/s means moving backwards at 15 metres every second. The equation When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. Velocity-time graphs The velocity of an object is its speed in a particular direction. Two cars travelling at the same speed but in opposite directions have different velocities. A velocity-time graph shows the speed and direction an object travels over a specific period of time. Velocity-time graphs are also called speed-time graphs. The vertical axis of a velocity-time graph is the velocity of the object. The horizontal axis is the time from the start. Features of the graphs When an object is moving with a constant velocity, the line on the graph is horizontal. When the horizontal line is at zero velocity, the object is at rest. When an object is undergoing constant acceleration, the line on the graph is straight but sloped. Curved lines on velocity-time graphs also show changes in velocity, but not with a constant acceleration or deceleration. The diagram shows some typical lines on a velocity-time graph. The steeper the line, the greater the acceleration of the object. The purple line is steeper than the green line because it represents an object with a greater acceleration. Notice that a line sloping downwards - with a negative gradient - represents an object with a constant deceleration (it is slowing down). Acceleration can be calculated by dividing the change in velocity (measured in metres per second) by the time taken for the change (in seconds). The units of acceleration are m/s/s or m/s2. The acceleration shown in the purple line can be calculated as follows: acceleration (m/s2) = change in velocity (m/s) ÷ time taken (s) = 10 ÷ 2 = 5 m/s2 This is the gradient of the purple line. We can calculate the acceleration shown in the first section of the green line as follows: acceleration (m/s2) = change in velocity (m/s) ÷ time taken (s) =8÷4 = 2 m/s2 This is the gradient of the first section of the green line. Here is a velocity-time graph: The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, you need to find the area of the light- blue triangle and the dark-blue rectangle. 1. Area of light-blue triangle The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation: area of triangle = ½ × base × height So, the area of the light-blue triangle is ½ × 8 × 4 = 16 m 2. Area of dark-blue rectangle The width of the rectangle is 6 seconds and the height is 8 metres per second. So, the area is 8 × 6 = 48 m 3. Area under the whole graph The area of the light-blue triangle plus the area of the dark-blue rectangle is: 16 + 48 = 64 m This is the total area under the distance-time graph. This area is the distance covered. Scalar and vector quantities A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector. Scalar quantities Scalar quantities only have magnitude (size). For example, 11 m and 15 ms-1 are both scalar quantities. Scalar quantities include:  distance  speed  time  power  energy Scalar quantities change when their magnitude changes. Vector quantities Vector quantities have both magnitude and direction. For example, 11 m east and 15 ms-1 at 30° to the horizontal are both vector quantities. Vector qualities include:  displacement  velocity  acceleration  force  weight  momentum Vector quantities change when:   their magnitude changes  their direction changes  their magnitude and direction both change The difference between scalar and vector quantities is an important one. Speed is a scalar quantity – it is the rate of change in the distance travelled by an object, while velocity is a vector quantity – it is the speed of an object in a particular direction. Example A geostationary satellite is in orbit above Earth. It moves at constant speed but its velocity is constantly changing (since its direction is always changing).  the difference in two vectors quantities = final vector - initial vector  the difference in two scalar quantities = large value - small value Equations and graphs Physics can be described as modelling the natural world using mathematics. In the case of moving objects, physics can accurately record and even predict the movement of objects using a set of physical laws and equations. These equations have helped launch space vehicles and are responsible for the realism of many computer games. Equations of motion The equations of motion relate to the following five quantities:  u - initial velocity  v - final velocity  a - acceleration  t - time  s - displacement Of the above u, v, a, and s are vector quantities. Time (t) is a scalar quantity. If any three of the five quantities are known then the other two may be calculated using the following four equations: If a question states 'from rest' what information about the equations is being given? Initial speed u = 0. Note the error in the science test. Acceleration = 9.8 ms-2 or -9.8 ms-2 due to gravity. Remember to have all your vectors in one direction as positive and make all the vectors in the opposite direction negative. Examples: An object lifts off vertically and takes a time of 4s to reach the highest point. What time will it take to fall back to Earth? 4 seconds – assuming no rocket force or air resistance. The acceleration due to gravity is the same in both directions, slowing down on the way up, speeding up on the way back down.