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Motion (Kinematics)

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Definition of Terms Motion – continuous change of position with respect to a certain reference point. Distance – refers to the total length of path (scalar quantity) Displacement – the straight-line distance between the starting and end points (vector quantity)

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Speed Speed is the rate at which an object moves Speed = distance/time Vs = d/t where Vs = speed d = distance t = time Example, if the cyclist moves 30 km in 2h, his speed is Vs = 30 km/2h = 15 km/h

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**Average Speed and Instantaneous Speed**

Vave = (V1 + V2 + … Vn)/n Instantaneous spped – the speed measured at a particular time or instant

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Velocity Velocity is defined as speed plus direction. It is a vector quantity Example: 80 km/h, northward In symbols, v = d/t where v = velocity d = displacement t = elapsed time

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Velocity versus Speed Speed and velocity are often used interchangeably; however, there is a clear distinction between these two concepts. Speed makes use of distance while velocity makes use of displacement. Because distance and displacement are different quantities, the magnitude of velocity will sometimes be different from that of speed. Speed and velocity will be equal in magnitude if the distance and displacement are also equal in magnitude.

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Example A car travels a distance of 40 km from Manila to a town in Laguna (south). Assume that the car traveled in constant speed. What is its average speed (in km/h) if traveling time is from 7:00AM to 7:30 AM? Its average velocity (km/h)? Suppose that after a business talk with a friend, the driver of the car drives straight back to Manila from 11:55AM to 12:20 PM. What was the car’s average speed (km/h) during the round trip? Its average velocity (km/h)

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**Solution Given: d1 = 40 km (1st trip) d2 = +40 km (return trip)**

t1 = 30 mins (1st trip) t2 = 25 min (return trip) Speed = d/t = 40km/30 min = km/min = 78km/h

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**Average velocity = -40km/0**

Average velocity = -40km/0.5hr) = - 78km/h from Manila to Laguna or southward Ave speed for the round trip = total distance during the round trip/total time spent for the roundtrip = (d1 + d2)/(t1 + t2) = (40km + 40km)/(30 mins + 25 mins) = 90km/h

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**The average velocity, v, for the round trip =**

total displacement for the round trip / time it takes for the total displacement for the roundtrip = [+40km + (-40km)] / 30min + 25 min = 0/50 mins = 0

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Exercises At the start of a trip, a car’s speedometer read 34,627 km, while at the end, it read 35,118 km. If the trip took 8hours, what was the car’s average speed assuming that the car moved at a constant rate? An airplane flies westward at a velocity of 220 km/h. If the wind is blowing southward with a velocity of 20 km/h, what is the resultant velocity of the airplane? A truck’s velocity was 60km/h, south. How far did it go after 15 mins? What was its total displacement?

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**Accelerated and Decelerated Motion**

Acceleration – change in velocity for every unit of time a = (vf – vi)/t

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Assignment 1-3. Choose the motion from a to d that matches with each scenario from the following situations a. The car speeds up c. The car decelerates b. Velocity is changed d. No fuel is consumed Which of the above happens when a driver steps on the accelerator? Which of the above happens when a driver steps on the brake? Which of the given situations happen when a driver turns around a rotunda?

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Assignment A car traveled at 88 km/h for 5 hours. How far did it travel? Mark walked 5 km/h. How long did it take him to travel 15 km? A ferryboat travels 90km in 45 mins. What is the average speed of the boat? A car has an initial velocity of 40 m/s. It stops over a distance of 120 m when the brakes are applied. How long does it take for the car to stop? What is the car’s deceleration? If it takes you half an hour to go 1 km across town, then what is your average speed?

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