- D ISTANCE & D ISPLACEMENT S PEED, VELOCITY & ACCELERATION Forces and Motion 2AB

R ECAP – S CALARS AND VECTORS Scalar quantities have magnitude (size) only E.g. Time, distance, speed, area  Vector quantities have both magnitude and direction ◦ E.g. Velocity, displacement, force, acceleration  Each of these need to be treated differently mathematically

D ISTANCE AND D ISPLACEMENT Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.scalar quantity Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.vector quantity

To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 metres east, 2 metres south, 4 metres west, and finally 2 metres north. Even though the physics teacher has walked a total distance of 12 metres, her displacement is?

D ISTANCE AND D ISPLACEMENT Distance is the actual distance covered Add or subtract distance like a scalar Displacement is the change in position Add or subtract displacement using vectors

Use the diagram to determine the resulting displacement and the distance travelled by the skier during these three minutes.

D ISTANCE AND DISPLACEMENT - EXAMPLE A swimmer completes a 100m race in 42 sec. The pool is 50m long. 1. Draw a vector diagram of this motion 2. What is the distance travelled at 0s, 21s & 42s? 3. What is the displacement of the swimmer at 0s, 21s & 42s?

S PEED AND V ELOCITY Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed is a scalar quantity that refers to how fast an object is moving.scalar quantity Average speed is the distance an object travels divided by the time it takes.

S PEED AND V ELOCITY Velocity is a vector quantity that refers to the rate at which an object changes its position.vector quantity Average velocity is the displacement of an object divided by the time it takes.

S PEED AND VELOCITY - EXAMPLE A swimmer completes a 100m race in 42 sec. The pool is 50m long. 1. What is the swimmers average velocity for the first 50m? 2. What is the swimmers change in velocity as he turns around? 3. What is the swimmers average velocity for the whole race?

I NSTANTANEOUS SPEED AND VELOCITY Instantaneous speed is how fast an object is moving at a particular instant in time: scalar Instantaneous velocity is how fast an object is moving and in what direction at a particular instant in time: vector Found by looking at a speedometer or by a police radar gun – hard to calculate!

A CCELERATION Acceleration is the rate at which an object changes its velocity. It is a vector quantity. Units: Note: remember to use negative numbers for vectors in the negative direction

A CCELERATION - EXAMPLE A cheetah running at 30ms -1 slows down as in approaches a stream. Within 3s, its speed has dropped to 9ms -1. Calculate the average acceleration of the cheetah.

S UMMARY Scalar quantities (units), symbol Vector quantities (units), symbol Distance (m), sDisplacement (m), s Speed (ms -1 ), v Velocity (ms -1 ), v Acceleration (ms -2 ), a Note: remember that vector quantities have direction relative to the starting point or origin.