2.1 Kinematics

Mechanics

Topic 2.1 Kinematics

Kinematic Concepts

DisplacementIs a measured distance in a given directionIt tells us not only the distance of the object from a particular reference point but also the direction from that reference pointIt is a vector quantityIn many situations it is measured from the origin of a Cartesian co-ordinate system

Kinematic Concepts

SpeedIs the rate of change of distanceOr the distance covered per unit timeSpeed is the total distance (d) covered in total time (t)Speed (s) = total distance (d)

total time (t)

Kinematic Concepts

VelocityIs the rate of change of displacementIs a measured speed in a given directionIt tells us not only the speed of the object but also the directionIt is a vector quantity

Average Velocity

Defined as the total displacement (s) of the object in the total time (t)Velocity (vav) = total displacement (s) total time (t)vav = s

tWhere indicates a small change in the value

Instantaneous Velocity

Is the velocity at any one instantv = s

tWhere t is tending towards zero

Kinematic Concepts

AccelerationIs the rate of change of velocity in a given directiona = v / t (where v = v – u)It is a vector quantityIf the acceleration of an object is positive then we understand its rate of change of velocity to be positive and it could mean that its speed is increasing Do not think of acceleration as a ´slowing up´or

a ´getting faster´.

Graphical Representation of Motion

These come in 4 forms1. Distance-time graphs2. Displacement-time graphs3. Velocity-time graphs4. Acceleration-time graphs

Gradiants of Graphs

Gradient of a Displacement-time graph is the velocity (instantaneous or average?)Gradient of a Velocity-time graph is the acceleration (instantaneous or average?)

Areas Under Graphs

Area under a Velocity-time graph is the displacementArea under a Acceleration-time graph is the velocityAreas can be calculated by the addition of geometric shapes

Uniformly Accelerated Motion

Velocity and hence Acceleration can be measured using Light gates Strobe photographs ( Duncan Page

142/3) Ticker tape timers

The Equations of Uniformly Accelerated Motion

There are 4 equations which we use when dealing with constant acceleration problemsI call them the “suvat” equationsYou need to be able to derive them

The 4 Equations

Supposing the velocity of a body increases from u to v in time t, then the uniform acceleration, a is given bya = change of velocity

time takena = v – u

t v = u + at - equation (1)

Since the velocity is increasing steadily, the average velocity is the mean of the initial and final velocities, i.e.Average velocity = u + v

2If s is the displacement of the body in time t, then since average velocity = displacement/time = s/tWe can say s = u + v

t 2 s = ½ (u + v) t - equation (2)

But v = u + at s = ½ (u + u + at) t s = ut + ½at2 - equation (3)

If we eliminate t from (3) by substituting in t = (v – u)/a from (1), we get on simplifyingv2 = u2 +2as - equation (4)

Knowing any three of s, u, v, a, t, and the others can be found

Experiments show that at a particular place all bodies falling freely under gravity, in a vacuum or where air resistance is negligible, have the same constant acceleration irrespective of their masses.This acceleration towards the surface of the Earth, known as the acceleration due to gravity, is donated by g.

Acceleration Due to Gravity

Its magnitude varies slightly from place to place on the Earth´s surface and is approximately 9.8ms-2

The Effects of Air Resistance

Air resistance depends on 2 things Surface area Velocity

Air resistance increases as surface area increasesAir resistance increases as the velocity increases

Terminal Velocity

As an object falls through the air, it accelerates, due to the force of attraction of the Earth. This force does not change.As the velocity increases, the air resistance, the force opposing the motion, increases, therefore the acceleration decreases.

If the object falls for long enough, then the air resistance (a force acting upwards) will equal the force of attraction of the Earth (the weight) (a force acting downwards)Now there are no net forces acting on the object (since the two forces balance) so it no longer accelerates, but travels at a constant velocity called its terminal velocity.

Terminal velocity depends on The size Shape And weight of the object

A sky diver has a terminal velocity of more than 50ms-1 (100 miles per hour)

Relative Motion

If you are stationary and watching things come towards you or away from you, then your stating velocities is easy.If, however you are in motion, either moving towards or away from an object in motion, then your frame of reference is different

In this case the relative velocity is the velocity of the object relative to your motion.Examples include cars overtaking Trains going passed platforms