Title TOPIC 8 LINEAR MOTION - WazaElimu.com.pdf ✅

67 No. DISTANCE DISPLACEMENT 1. This is the length between two points taken by a body while in motion This is the distance covered in a particular direction 2. Scalar quantity Vector quantity NOTE: Both distance and displacement has the same SI – Unit. Example Glory runs round a circular track of length 500m (a) What distance does she cover? (b) What is her displacement from the starting point? Solution (a) Distance is actual ground covered. Distance = Length of track x 2 Distance = 500m x 2 Distance = 1000m (b) Displacement means how far she is from the starting point. Since she ends the race at the starting point, the displacement is zero (o). SPEED AND VELOCITY 1. SPEED (V)  This is the rate of change of distance. OR  This is the distance covered per unit time. Speed (V) = Distance (d) Time (t) o SI – Unit of speed is m/s o Speed may also be measured in km/h or cm/s NOTE:  During your journey you do not maintain the same speed at all time, this is why the term “Average velocity” is normally used. 2. VELOCITY (V)  This is the rate of change of displacement. OR  This is the rate of change of distance moved in a specific direction. OR V= d t
68  Velocity is the speed in a specific direction. Velocity (V) = Displacement (S) Time (t) Also: Where by: U = Initial velocity V = Final velocity INITIAL VELOCITY  This is the starting velocity FINAL VELOCITY  This is the finishing velocity  The SI – Unit of average velocity is the as the unit of average speed, that is m/s NOTE:  Velocity at a particular instant of time is called instantaneous velocity.  A body is said to move with uniform velocity if its rate of change of displacement with time is constant. Example 1 An object travelled 20m to the right in 4 seconds and then 12m to the left in 3 seconds. For its total motion, what was the average speed and average velocity? Solution  When the object is moving to the right, its displacement is positive and when moving to the left it is negative. Time is always positive. o Total distance travelled (d) = 20m + 12m = 32m o Total displacement travelled (s) = 20m + (−12m) = 8m o Total time take for both distance and displacement = 4sec + 3sec = 7sec Then; Average speed (v) = Distance (d) Time (t) V= 32m 7sec = 4.57m/s The average speed = 4.57m/s Average velocity (V) = Displacement (S) Time (t) V = 8m 7sec = 1.14m/s The average velocity = 1.14m/s Example 2 A ball dropped from a height of 20m above the ground. It hits the ground in 2 sec and bounces back up to a height of 12.7m in 1.6 sec. What is its average velocity? Solution  When the object is moving up, its displacement is positive and when moving down it is negative. S = −20m t = 2 sec S = +12.7m t = 1.6 sec Ground level Total displacement (S) = −20m + 12.7m = −7.3m Total time taken (t) = 2 sec + 1.6 sec = 3.6 sec Then: Average velocity (V) = Displacement (S) Time (t) V = −7.3m 3.6 sec = −2.03m/s The average velocity for the entire motion = 2.03m/s V = S t Average velocity = U+V 2