Dynamics (Linear Kinematics) Kinematics and Kinetics of a particle motion A Particle All points on the body move with the same motion: same displacement, velocity and acceleration. To simple analysis and calculation, the body such as an aeroplane, a train or an aircraft carrier can be assumed as a particle.
Kinematics Kinematics: In studying the kinematics, we describe only the motion of the particle without considering the forces that act upon it, i.e.; we study the variations of the particle’s position, velocity, and acceleration with the time.
Displacement versus Distance Distance is a scalar quantity that expresses only the length of an arbitrary path. Displacement is the vector that specifies the position of a point or a particle.
Velocity versus Speed Velocity is the measurement of the rate and direction of change in the position of an object. It is a vector quantity both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is known as speed.
Acceleration Acceleration is the vector quantity describing the rate of change with time of velocity.
Straight Line Motion with Constant Acceleration
v u at u v v avg 2 s ut 12 at 2 v 2 u 2 2as Example 1: A particle is moving in a straight line from O to A with a constant acceleration of 2 ms -1. Its velocity at A is 30 ms-1 and it takes 15 seconds to travel from O to A. Find (a) the particle’s velocity at O (b) the distance OA Example 2: An automobile initially moving at 30 ft/s accelerates uniformly at 15 ft/s2. (a) How fast is it moving after 3s? (b) At the end of the 3s interval, the driver hits the brakes and now accelerates at -30 ft/s2. How long does it take to come to a complete stop? Example 3: A man walks for 35 minutes at 6.5 km/h and then 45 minutes at 4.5 km/h. Determine his average speed in m/s. MIET 6316C Apply basic scientific principles College of Science, Engineering and Health School of Engineering (TAFE)
Class Notes 1
Prepared by Yadana Wai
Example 4: How long does it take a car to cross a 30 m wide intersection after the light turns green, if the car accelerates from rest at a constant 2.00 m/s2?
Example 5: You are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before take-off at least 27.8m/s, and can accelerate at 2.00 m/s2. (i) If the runway is 150 m long, can this airplane reach the required speed for take-off? (ii) If not, what minimum length must the runway have? Example 6: A goods-train leaves Newcastle bound for Sandy and reaches its maximum speed of 40 km/h in one minute. Five minutes later an express train leaves Sydney bound for Newcastle and reaches its maximum speed of 90 km/h in one minute. Assuming the rates of acceleration were constant and that the maximum speeds were maintained for the rest of the journey, find (a) the acceleration of each train (b) their distance apart fifteen minutes before meeting.
Freely Falling Bodies Suppose an object is released either from rest or with an initial upward or downward velocity, and after release it is acted on only by the pull of gravity. If the air resistance is negligible, the object is said to be in free fall. Examples are a ball dropped from a height, a rock thrown vertically upward, and an arrow shot straight down from a height. All free fall objects have the same constant acceleration vertically downward. The magnitude of this gravitational acceleration is 9.8 m/s2 in SI unit and 32.2 ft/s2 in imperial unit. Example 7: A rivet is dropped from a building 50 m height. (a) If it is falling freely under gravity how long will it take to reach the ground? (b) What will be its velocity at the instant just before touching the ground? Example 8: A tourist drops a rock from rest from a guard rail overlooking a valley. What is the velocity of the rock at 4.0 s? What is the displacement of the rock at 4.0 s? Example 9: In a 1979 movie, a stuntman leaped from a ledge on Toronto’s CN Tower and experienced free fall for 6.0 s before opening the safety parachute. Assuming negligible air resistance, determine the stuntman’s velocity after falling for (a) 3.0 s and (b) 6.0 s.
MIET 6316C Apply basic scientific principles College of Science, Engineering and Health School of Engineering (TAFE)
Class Notes 2
Prepared by Yadana Wai
Curvilinear Motion (Projectile Motion) Projectile motion is a part of parabolic motion. Projectile motions are under constant acceleration. Throughout the motion, the horizontal component of the velocity is constant and vertical component of the velocity is changing with constant gravitational acceleration.
Example 10: A high-altitude bomber lines up on its target 4900 m below. If the bomb scores a direct hit, calculate the angle between the vertical and a line joining the bomber and its target at the instant of release. The bomber’s velocity was 360 km/h horizontally at the time of release.
Example 11: A long-jumper leaves the ground at an angle of 20.0° above the horizontal and at a speed of 11.0 m/s. (a) How far does he jump in the horizontal direction? (Assume his motion is equivalent to that of a particle.) (b) What is the maximum height reached?
MIET 6316C Apply basic scientific principles College of Science, Engineering and Health School of Engineering (TAFE)
Class Notes 3
Prepared by Yadana Wai
Example 12: A stone is thrown from the top of a building upward at an angle of 30.0° to the horizontal and with an initial speed of 20.0 m/s, as shown below. If the height of the building is 45.0 m, (a) how long is it before the stone hits the ground? (b) What is the speed of the stone just before it strikes the ground?
MIET 6316C Apply basic scientific principles College of Science, Engineering and Health School of Engineering (TAFE)
Class Notes 4
Prepared by Yadana Wai
