Speed, Distance and Time

Speed and Velocity An object has speed when it travels a distance in a time interval. An object has speed when it travels a distance in a time interval. At any moment in time, a moving object has instantaneous speed. Since this is difficult to calculate, we usually use average speed. At any moment in time, a moving object has instantaneous speed. Since this is difficult to calculate, we usually use average speed.

Speed and Velocity Since velocity is speed in a given direction, Since velocity is speed in a given direction, the equation for average velocity is: the equation for average velocity is: final distance – initial distance final distance – initial distance Velocity = final time – initial time final time – initial time ∆d ∆d V av = V av = ∆t ∆t The unit for speed or velocity is metres per second (ms -1 ) or kilometers per hour (kmh -1 ). The unit for speed or velocity is metres per second (ms -1 ) or kilometers per hour (kmh -1 ).

Distance and Time Distance is a measurement of how far apart two points are. Distance is a measurement of how far apart two points are. The unit for distance is the metre (m), or kilometer (km). The unit for distance is the metre (m), or kilometer (km). Displacement is a measurement of how far an object has moved from its starting point. Displacement is a measurement of how far an object has moved from its starting point.

Distance and Time The equation is: The equation is: displacement = final – initial distance distance Time is a measurement of the duration of an event. Time is a measurement of the duration of an event. The unit for time is the second (s), or hour (h). The unit for time is the second (s), or hour (h).

Distance-Time Graphs Distance is plotted on the vertical axis and Time on the horizontal axis. Distance is plotted on the vertical axis and Time on the horizontal axis. The distance-time graph for an object moving at a constant speed is always a straight line with a slope. The distance-time graph for an object moving at a constant speed is always a straight line with a slope.

Interpreting Distance/time graphs t d Stationary Constant (v=0) (the distance remains the same) the gradient of a distance/time graph is the velocitythe gradient of a distance/time graph is the velocity

Interpreting Distance/time graphs t d Constant velocity (the distance changes at a constant rate) Faster constant velocity Slow constant velocity

Interpreting Distance/time graphs t d Changing velocity (the distance moved per second changes) Slowing down (-ve acceleration) Speeding up (+ve acceleration)

Interpreting Distance/time graphs t d An object that is returning to its starting point. (at a constant speed)

Interpreting Distance/time graphs A -fast constant speed (steep gradient and line straight) A -fast constant speed (steep gradient and line straight) B –slower constant speed (shallow gradient and line straight) B –slower constant speed (shallow gradient and line straight) C –stationary (line horizontal) C –stationary (line horizontal) D –Very fast constant speed backwards (steep gradient, straight line, sloping down) D –Very fast constant speed backwards (steep gradient, straight line, sloping down) t d A B C D RC Car Journey

Calculating Gradient The slope or gradient of a line can be calculated using the formula: The slope or gradient of a line can be calculated using the formula: Gradient = Increase in vertical height (of line) Increase in horizontal length Gradient = Increase in vertical height (of line) Increase in horizontal length

Velocity (speed) Velocity (speed) is a measure of how quickly the position of an object is changing (units ms -1 ) If the object is a constant velocity (balanced forces) the formula is; If the object is a constant velocity (balanced forces) the formula is;

Velocity (speed) If the velocity of a journey changes (some slowing and speeding up) the formula for the average velocity is; If the velocity of a journey changes (some slowing and speeding up) the formula for the average velocity is;

Velocity Calculations 1.A cyclist travels 50km in 1.5 hours. Calculate her velocity. 2.An athlete records a time of 64s for a 400m race. What speed was he running at? 3.An Otago student takes 2.5 hours to return to Dunedin from Timaru (190km), with a short stop at Hampden from fish and chips. What was her average velocity for the journey?

Acceleration An object changing its speed is said to be accelerating. If the acceleration is: An object changing its speed is said to be accelerating. If the acceleration is: – positive (eg. 2ms -2 ) = object speeding up – negative (eg. -2ms -2 ) = object slowing down or decelerating

Acceleration The equation is: The equation is: final speed – initial speed acceleration= acceleration= time taken time taken ∆v ∆v a = a = ∆t ∆t The unit for acceleration is metres per second squared (or ms -2 ). The unit for acceleration is metres per second squared (or ms -2 ).