Speed Velocity and Acceleration Everything You Need To Know About Motion

Motion Motion is just a change in position. To describe how an object moves you need A ruler to measure where an object is. And a clock to measure when an object is.

Here is a little bug located at 0 cm at 0 seconds.

10 seconds later he is at 50 cm.

SPEED The speed of the bug is just his distance traveled divided by how long it takes. Speed = distance/time Speed = 50 cm/10 s = 5 cm/s

Speed is just how fast something is moving. Speed is always a positive number. Quantities that can be described by a single number are called scalars.

MORE SCALARS TEMPERATURE VOLUME MASS STUDENTS IN A ROOM ENERGY

VELOCITY Velocity is speed and direction. Velocity is how fast and which way. Quantities that have direction are called vectors.

MORE VECTORS ACCELERATION FORCE DISPLACEMENT MOMENTUM

Suppose our bug starts off at 100 cm.

And ends up at 80 cm 10 seconds later.

Velocity = change in position/time Calculating velocity is a little more complicated than calculating speed. Velocity = change in position/time Velocity = (final position – initial position)/time Velocity = (80cm – 100cm)/10 seconds Velocity = - 2 cm/s

For objects moving along a straight line A positive velocity means moving to the right. (usually) A negative means moving to the left. (usually)

A negative velocity does not mean an object is moving slower than zero cm/s. You can’t move slower than standing still. It just means an object is moving in a certain direction.

ACCELERATION Acceleration is a change in velocity. So an object accelerates if it Speeds up Slows down Or changes the direction it is moving,

Acceleration = change in velocity/time Acceleration = (final velocity – initial velocity)/time Acceleration has units of velocity/time (meters per second)/seconds Or m/s/s or m/s2

confusion Acceleration, like velocity, has direction. For objects moving along a straight line the direction of an object’s acceleration is denoted by plus or minus.

Acceleration = (30 m/s – 0 m/s)/10 s a = 3 m/s/s The car’s velocity is increasing 3 m/s per second. The car is accelerating towards the right.

a = (0m/s – 20 m/s)/10 s a = - 2 m/s/s Although the car is moving to the right It is accelerating to the left!

a = (final velocity – initial velocity)/time a = ( -30 m/s – 0 m/s)/ 10 s a = - 3 m/s/s The car is both moving to the left and accelerating to the left. Negative acceleration does not always mean an object is slowing down!

Newton’s 3 laws of motion Isaac Newton 1642 --- 1727

1st Law: Law of Inertia A body at rest tends to stay at rest, a body in motion tends to keep moving along at a constant speed and in a straight-line path unless interfered with by some external forces.

example

Motorcycle crash dummy

Another example (watch the ladder)

2nd Law: F=ma The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.The direction of the acceleration is in the direction of the applied force.

Directly proportional to Force Small force Small acceleration Large force Large acceleration

inversely proportional to mass Beach ball Bowling ball small mass Large acceleration Large mass Small acceleration

“Inertial” mass “Inertial” mass, mi, is the resistance to changes in the state of motion Objects with large mi are hard to get moving (& once started, hard to stop), Objects with small mi easier to get moving (& easier to stop),

Units again! (we cant avoid them!) Mass: basic unit = 1kilogram = 1kg mass of 1 liter (1.1 quarts) of water 10cm This much water! 10cm 10cm

Slide tail of one to tip of the other (keep directions fixed) Net force Tip-to-tail method for adding vector Net force is the vector from the tail of the 1st to the tip of the 2nd. (0 in this case). Slide tail of one to tip of the other (keep directions fixed)

Tip-to-tail method Net force points down the hill Slide tail of one to tip of the other (keep directions fixed)

Newton’s 2nd law  F=ma a  F a  F a  1/m a  F/m a = F/m a is proportional to F: a  F direction of a = direction of F: a  F a is inversely proportional to m: a  1/m combine: a  F/m multiply both sides by m set proportionality constant = 1: a = F/m

Weight = Force of gravity Free-fall acceleration of a beach ball & a bowling ball are the same: a=g m M Beach ball Bowling ball F2 = Ma a = g F1 = ma a = g Bowling ball has more inertia: M > m Force of gravity must be larger on the bowling ball by a factor that is proportional to mass

Weight is proportional to mass Newton’s 2nd law: F=ma If gravity is the only force: F = W a = g W = mg acceleration due to gravity weight “gravitational” mass

Two different aspects of mass Force of gravity is proportional to “gravitational” mass mgg Weight: W = m g Newton’s 2nd law: Inertia; resistance to changes in state is proportional to “inertial” mass F m a = mi Experiment shows: mg = mi

Units of Force F=ma m kg s2 1 pound =1lb = 4.5 N Unit of force: 1 Newton = 1N = 1 kg m/s2 1 pound =1lb = 4.5 N

What is your mass? F=ma W=mg a=g m= W W g Weight = force of Earth’s gravity on you Suppose I jump off a tqble F=ma W=mg a=g m= W g W

Kgf =“kilogram force” = 9.8 N !!!!! Mass & weight “weight” = 85 kg kg is a unit of mass, not force “my weight” Convert to Newtons: W = 85 kg x 9.8m/s2 = 833 N = Units of N kg m/s2 Kgf =“kilogram force” = 9.8 N

Newton’3rd Law: action-reaction Whenever one object exerts a force on a second object, the second object exerts an equal in magnitude but opposite in direction force on the first. reaction: the canoe pushes me forward action: I push on the canoe

Action Reaction

I push on the bus v= 0 F

But I accelerate v Newton: The bus exerted an “equal but opposite” force on me.

This force tries to accel. Look again All forces come in pairs! -F F This force causes me to accelerate backwards This force tries to accel. the bus forward

Air-filled balloon reaction: air pushes on balloon action: balloon pushes on air

opposite force on the gun F1 recoil action: gun exerts force F2 on bullet making it accelerate reaction: equal but opposite force on the gun F1 Produces a recoil

Rocket propulsion reaction: rocket gets pushed in the opposite direction action: rocket engine pushes exhaust gasses out the rear