Mechanics

Mechanics - is a branch of physics that deals to the study of force and motion. Motion - is a continuous change in position with respect to a certain reference point. (Albert Einstein) *According to Einstein- Motion is relative- “A body can be moving with respect to the first-body but at the same time can be at rest or be moving at different speed with respect to the second-body”. A. Uniform Motion – is a motion of the body that moves at constant velocity. (a = 0) B. Uniformly Accelerated motion – is a motion of the body that moves in a changing velocity.(a= +, -) Rectilinear Motion(One-dimensional motion) - is a motion along straight-line path. 1. Distance – is a scalar quantity that describe how far “something” has traveled.( units: cm, m, km, in., ft., mi,etc. ) 2. Displacement – is a vector quantity that describes how far “something” has traveled and in to what direction.( d = x2 – x1, units: cm, m, km, in., ft., mi,etc. ) 3. Speed – is a scalar quantity that describe how fast “something” has traveled. ( s = d/t, units: cm/s, m/s, km/h, mi/h, ft/s, in/s, etc.) 4. Velocity – is a vector quantity that describe how fast “something” has traveled and in to what direction. – is the change in displacement divided by the change in time( v = ∆d/∆t or d2 – d1/ t2 – t1 ), units: cm/s, m/s, km/h, mi/h, ft/s, in/s, etc.) 5. Average Speed – is the total distance traveled divided by the total time covered. ( sav = dT/tT, units: cm/s, m/s, km/h, mi/h, ft/s, in/s, etc.) 6. Instantaneous Speed – is the speed that “something” has at any one instant. (units: cm/s, m/s, km/h, mi/h, ft/s, in/s, etc.) example: the speed registered by your speedometer. 7. Average Velocity – a.) vav = (v1 + v2) / 2 b.) vav = (d2 – d1) / t 8. Acceleration – is a vector quantity that define as “the rate of change of velocity” or “ the change in velocity divided by the change in time”. a = ∆v/∆t or (v2 – v1) / (t2 – t1 ), units: m/s2, cm/s2, in/s2, ft/s2, km/hr2, mi/hr2) Motion in a Straight-Line Graph: A. d-t Graph (slope of the line m = velocity v) a.) d

t - m=+=v - the body is moving at constant positive velocity(uniform motion)

b.) d

t - m=-=v - the body is moving at constant negative velocity(uniform motion)

c.) d

t - m=0=v - the body is in at rest position

B. v-t Graph (slope of the line m = acceleration) a.) v

t - m=+=a - the body is moving at increasing velocity(uniformly accelerated motion)

b.) v

c.) v

t - m=-=a - the body is moving at decreasing velocity(uniformly accelerated motion)

t - m=0=a - the body is moving at constant velocity (uniform motion)

Problems in Rectilinear Motion: A. Speed 1. If the continents are drifting apart at constant speed of 3 cm/yr, Africa and South America are separated by 6.4 x 108 cm, how long has this drift been occurring? 2. Sound cause by an explosion at the oceans surface travels vertically down to the bottom, is reflected back and return to the surface in 11.6 seconds. Calculate the depth of the ocean if sound travels at 1450 mi/s in water. 3. A woman standing in front of a cliff claps her hands and after 3.8 seconds she hears an echo. How far is the woman from the cliff if the sound travels at 343 m/s in air? B. Average Speed 1. A person drives for 50 min. at a speed of 28 m/s, then stops for 20 min., and finally drives for 36 m/s. Calculate a.) the total distance traveled and b.) the average speed. 2. A train leaves a station and travels at 80 mi/h for 3.5 h and then 70 mi/h for 2 h to reach its destination. What was the trains average speed for the entire trip? 3. An airplane flies 600 km away from its base at 200 km/h, then flies back to its base at 300 km/h. What is its average speed? 4. A car travels at 40 km/h for 2 h, at 50 km/h at 1 h, and at 20 km/h at 0.5 h. What is the cars average speed? C. Acceleration 1. In 2.5 s a car increases its speed from 60 km/h to 65 km/h. While a bicycle goes from rest to 1.389 m/s. Which undergoes a greater acceleration and what is the acceleration of each vehicle? 2. A particular car can go from rest to 90 km/h in 10 s. What is its acceleration? Express your answer in m/s2. 3. What is the acceleration of the vehicle that changes its velocity from 100 km/h to a dead stop in 10s? 4. How long does a car with an acceleration of 2 m/s2 takes to go from 10 m/s to 30 m/s? Uniformly Accelerated Motion: a.) v2 = v1 + at b.) d = v1t + ½ at2 c.) d = [ (v1 + v2) / 2 ] t d.) v22 = v12 + 2ad Problems: 1. A car has an initial velocity of 20 m/s and an acceleration of -1 m/s. Find its a. velocity after 10 seconds b. velocity after 50 seconds c. displacement after 10 seconds d. displacement after 50 seconds e. displacements when it comes to a stop 2. The driver of a train traveling at 30 m/s applies the brakes when he passes an amber signal. The next signal is 1.5 km down the track and the reaches it 7 5 seconds later. Assuming uniform acceleration, find the velocity of the train at the second signal. 3. A golf cart has an acceleration of 0.4 m/s2. What is its velocity after it has covered 10 m starting from rest? 4. A bus moving at a speed of 20 m/s begins to slow at a rate of 3 m/s each second. Find how far it goes before stopping. 5. A skier starts from rest and slides 9 m down a slope in 3s. In what time after starting from rest will the skier acquire a velocity of 24 m/s? Assume constant acceleration?