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IB-Physics-Core-Notes Topic 2 Mechanics 2.1 Kinematics 2.1.1 Define displacement, velocity, speed and acceleration. Displacement- Defined as the change in position of an object. Displacement is a quantity that has both direction and magnitude, it is a vector. Measured in metres. Speed- How far an object travels in a given time. Rate of change of distance (ms-1) Velocity- The vector version of speed. Tells us the magnitude of how fast an object is moving and the direction in which it is moving. (ms-1) AverageVelocity  Displacement TimeElapsed Acceleration- Rate of change of velocity (ms-2) AverageAcceleration  ChangeInVelocity TimeElapsed 2.1.2 Explain the difference between instantaneous and average values of speed, velocity and acceleration. Instantaneous values of velocity speed and acceleration are taken at a particular moment. In any realistic situation they will be constantly varying and is not always meaningful or useful to know this e.g. drivers need to keep their instantaneous speed below the speed limit. Average velocity, speed and acceleration are taken over a certain period of time or distance. E.g. Average speed between Porto and Lisbon = distance/time = 350/km/3 hours 30 min = 100 kmh-1 2.1.3 Outline the conditions under which the equations for uniformly accelerated motion may be applied. The following equations of motion may be applied to an object that has a constant acceleration. a  (v  u) t s  ut  1 at 2 v 2  u 2  2as v= final velocity/ ms-1) u= initial velocity / ms-1 a= acceleration/ ms-2 s= displacement/m t=time/s 2.1.4 Identify the acceleration of a body falling in a vacuum near the Earth’s surface with the acceleration g of free fall. Free fall is the uniform acceleration (ignoring the effect of air resistance) in the vertical direction of an object in a uniform gravitational field. All falling objects have the same acceleration independent of their masses. On earth all objects accelerate towards the ground at 9.81 ms-2. Acceleration due to gravity can be measured in a number of ways. In the arrangement that is shown a timer starts when the ball is released form an electromagnet and stops when the ball passes through a gate at the bottom. The acceleration due to gravity can then be calculated using: g  2s t 2 Acceleration due to gravity can also be calculated using light gates of ticker timers. 2.1.5 Solve problems involving the equations of uniformly accelerated motion. This question is about throwing a stone from a cliff. Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards. v = 8.0ms –1 Sea The stone leaves Antonia’s hand with a speed v = 8.0ms–1. The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the point where the stone leaves Antonia’s hand. (a) Ignoring air resistance calculate (i) the maximum height reached by the stone. v 2  u 2  2as v 2 s  2s 82 s  2 10 s  32.m (2) (ii) the time taken by the stone to reach its maximum height. a  v  u t t  v  u a t  8 10 t  08.s (1) The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s. (b) Determine the height of the cliff. Time to go form top of cliff to sea = 3.0 – (2 x 0.8) = 1.4s s  ut  1 at 2 s  (80. 1.  ( 1 10 14.2 ) s  21m (3) (Total 6 marks) 2.1.6 Describe the effects of air resistance on falling objects. Air resistance acts upon all moving objects. As the velocity of an object increases the size of the air resistance also increases. Eventually the force of air resistance will equal the force of gravity. When this happens the object will stop accelerating. It has reached its terminal velocity. The terminal velocity of an object is dependant on its shape. A feather has a lower terminal velocity than a hammer. 2.1.7 Draw and analyse distance–time graphs, displacement–time graphs, velocity–time graphs and acceleration–time graphs. Displacement – time graphs The gradient of a displacement - time graph is the velocity. Velocity – time graphs The gradient of a velocity – time graph tells the acceleration of the object. If the line is flat the object is travelling at a constant velocity. The area under the graph represents the distance travelled. Acceleration – time graphs The area under an acceleration – time graph represents the change in velocity. 2.1.8 Calculate and interpret the gradients of displacement–time graphs and velocity–time graphs, and the areas under velocity–time graphs and acceleration–time graphs. 1) The graph shows the variation with time t of the velocity v of an object. v t Which one of the following graphs best represents the variation with time t of the acceleration a of the object? A. B. C. D. 2) An athlete runs round a circular track at constant speed. Which one of the following graphs best represents the variation with time t of the magnitude d of the displacement of the athlete from the starting position during one lap of the track? A. d B. d 0 0 0 t 0 t D. d