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Objectives After completion, you should 1. Know the term displacement, velocity,acceleration and deceleration for motion in a straight line 2. Be familiar with displacement – time graph. Graphical representation 1 Displacement – time graph (t,x) Displacement is a distance together with a direction. Displacement is a vector. Velocity is a speed together with a direction Velocity is a vector

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Velocity and Displacement For example, two cars travelling in opposite direction on the M1 motor way may have the same speed 65 miles per hour (mh -1 ), but they have different velocities. For velocity we have to include whether the car is going on the north bound or the south bound. For convenient, we only use positive or negative direction. Displacement Suppose a body is moving along a straight line. Its position relative to fixed origin is called its displacement. ABAB DisplacementAB= s.

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Distance and Displacement Be careful with the distinction between distance and displacement. If a body travels 5m from the origin and then returns to the origin, It has travelled through a distance of 10m, but its displacement is 0 m. Units The units used in mechanics are metres (m) for displacement, seconds (s or sec) for time and metres per second (ms -1 ) for velocity, sometimes kmh -1 for speed which can easily be converted into ms -1. O P 5m

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Displacement – time graph and Distance –time graph A girl walks 10m due positive direction in 5 seconds then stops for 2 seconds and finally walks 15m due negative direction in 5 seconds. Draw a displacement – time graph and distance – time graph. Average speed =Average velocity = = -5/12 =-0.417 m/s = 25/12 = 2.08 m/s Displacement-time graph: The gradient represents velocity. Distance-time graph: The gradient represents speed.

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Displacement – time graph :(t, x) Example 1 A cyclists journey is shown on (t, x) graph. Describe the motion. B A C D E A:A starts from rest( t = 0, x = 0) B: Travels 10 km in 1 hour at a velocity 10 km/h. C: Rests for 30 minutes (v = 0) D: Cycles 6 km in ½ hour at a velocity of 12 km/h. E: Returns to starting position, cycling 16 km in 1 hour at a velocity -20 km/h.

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Displacement – time graph :(t, x) Example 2 A cyclist starting from a point A travels 300 m due north (positive direction) to a point B at constant speed of 6 m/s. She rests at B for 40 seconds and then travels 500 due south (negative direction) to a point C at a constant speed of 10 m/s. (a) Draw a displace – time graph (b) Total distance travelled =800 m (c) Average speed = (a) Total time taken = 140 secs 800/140 =5.71 m/s (d) Increase in displacement = 300 – 500 = -200 (e) Average velocity = -200/140 = -1.43m/s

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