Introduction• Dynamics includes: - Kinematics: study of the motion (displacement, velocity, acceleration, & time) without reference to the cause of motion (i.e. regardless of forces). - Kinetics: study of the forces acting on a body, and the resulting motion caused by the given forces. • Rectilinear motion: position, velocity, and acceleration of a particle as it moves along a straight line. • Curvilinear motion: position, velocity, and acceleration of a particle as it moves along a curved line. 2
Curvilinear MotionA particle moving along a curve other than a straight lineis said to be in curvilinear motion. http://news.yahoo.com/photos/ss/441/im:/070123/ids_photos_wl/r2207709100.jpg3
Activityage 228, Q. 1-8age 196, Q. 1-3ab: Walking Uniformlyab: Acceleration due to Gravity
Final Velocityelocity can be calculated if we consider itin terms of the initial velocity which hasundergone acceleration or deceleration.= u + at= final velocity, in m/s= initial velocity, in m/s
Activityhat is the final velocity of a person walkingat 4 m/s who accelerates at 1 m/s 2 for 5 s?= u + at = 4m/s + 1m/s2 x 5s = 4m/s + 5m/s
Distance Coveredistance can be determined if the initialvelocity, time and acceleration are known.= ut + ½ at2= distance, m= initial velocity, m/s
Activityhat is the depth of a well, if when you dropa rock, it takes 5 seconds to hit thebottom?= ut + ½ at2 = 0(5) + ½ (9.81m/s2)(5s)2 = 0 + ½ (9.81)(25)
Vertical MotionNLY in situations where objects aremoving vertically through space, is theacceleration - 9.81 m/s2.n object dropped has an initial velocity of 0m/s.he acceleration due to gravity slowsobjects moving upwards and speeds upobjects moving downwards.
Final Velocityhe final velocity can also be calculated thisway.2 = u2 + 2as = final velocity, m/s = initial velocity, m/s
Short Cuthat is the final velocity of a car if it starts at10 m/s and accelerates at 2 m/s2 over adistance of 100m?2 = u2 + 2as = (10 m/s)2 + 2(2m/s2)(100m) = 100 + 400
Exam QuestionFrom the top of a tower an object is thrown vertically downward with a velocity of 20 m/s.What is the velocity of the object after it has fallen 60 metres? A) 55 m/s B) 50 m/s C) 45 m/s D) 40 m/s
Exam QuestionA motorcyclist, travelling at a speed of 30 m/s, sees an obstacle 100 metres in front of him andputs on the brakes. He hits it 5.0 seconds later.If the motorcycle slows down uniformly, how fast was it going at the instant of the collision? A) 10.0 m/s B) 8.0 m/s C) 6.0 m/s D) 4.0 m/s
Activityage 234, Q 1-5age 238, Q 1-6andout
Sample ProblemBall tossed with 10 m/s vertical velocity from window 20 m aboveground.Determine:• velocity and elevation above ground at time t,• highest elevation reached by ball and corresponding time, and• time when ball will hit the ground and corresponding velocity. 16
ExampleA projectile is fired from the edge of a 150-m cliff with an initialvelocity of 180 m/s at an angle of 30° with the horizontal. Find(a) the range, and (b) maximum height. y Remember:v = v0 + atx = x0 + v0t + at 1 2 2v = v + 2a ( x − x0 ) 2 2 0 x 17
Summaryhen air resistance is negligible, all freelyfalling objects have the same downwardacceleration.ball rolling down an incline has uniformacceleration.cceleration due to gravity has a value of9.81 m/s2.
Summary negative slope on a straight line position-time graph indicates motion in a negativedirection at constant velocity.verage velocity = displacement/time interval which can be taken at any 2 times on aposition-time graph.verage speed = total distance/time interval
Summaryelocity is a vector quantity which may befound if the velocity is uniform, with velocity = displacement/time.peed is a scalar quantity which may befound, if the speed is uniform, with speed = distance/time.he position-time graph for an objectmoving with uniform motion is a straight
Summarycceleration is the rate of change of velocityover time.=Δ /עΔt = (1/)ע2 -עΔtn velocity-time graphs, a straight lineshows that an object has a constantacceleration.
Summary negative slope on a velocity-time graphmeans that the magnitude of the velocityis decreasing, if the object is moving in apositive direction.he area under the velocity-time graphgives the displacement.= u + at
Summaryf the motion is in a straight line, the vectornotation may be omitted and +/- signsused instead. curved velocity-time graph indicates achanging acceleration. The averageacceleration for an interval is found byfinding the slope between two points onthe graph.
Summaryhe acceleration at any point on a curvedvelocity-time graph is the slope of the tangent tothe curve at that point.o construct a velocity-time graph from a tickertape recording, mark the tape into lengths of thesame time interval. The displacement for eachinterval divided by the time gives the averagevelocity for that interval. Plotting the averagevelocity for each interval versus the time willyield a velocity-time graph.
Exam QuestionA diver jumps from a height of 3.0 metres above the height of the water and touches the surface1.0 s later.What was his velocity when he hit the water? A) 8.0 m/s B) 7.0 m/s C) 6.0 m/s D) 5.0 m/s