Kinematics (2)

Position

Where object is at time, relative to reference frame

$$Displacement$$

Change in position of an object. Has a direction and magnitude (+ or - based on direction)

$\Delta$ x = xf - xo

Displacement = final position - initial position

Distance & distance travelled

Magnitude of displacement

Distance travelled is the total length of the path travelled (can be greater than the magnitude of the displacement)

A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is their displacement? (b) What distance do they ride? (c) What is the magnitude of their displacement?

(a) The rider’s displacement is Δ⁢𝑥=𝑥f−𝑥0=−1km. (The displacement is negative because we take east to be positive and west to be negative.)

(b) The distance traveled is 3km+2km=5km.

(c) The magnitude of the displacement is 1km.

Vectors

Any quantity with both magnitude and direction

Direction in 1D motion given by + or -

Represented by arrows

Time & elapsed time

Interval over which change occurs

Elapsed time Δ⁢𝑡 is the difference between the ending time and beginning time,

Δ⁢𝑡=𝑡f−𝑡0

Average & instantaneous velocity

Average: displacement (change in position) divided by the time of travel,

$$v=\frac{\Delta x}{\Delta t}=\frac{xf-xo}{ti-‎to}$$

Instantaneous: is the average velocity over an infinitesimally small time interval (typically requires limits/calculus)

Instantaneous & average speed

Instantaneous: magnitude of instantaneous velocity

Average: distance traveled divided by elapsed time (can be greater than average velocity. E.g. driving from home to store and back, zero displacement = zero velocity)

Average acceleration

Rate at which velocity changes in m/s²

ā$=\frac{\Delta v}{\Delta t}$

A change in velocity can be a change in magnitude (or speed), but it can also be a change in direction

Deceleration vs. Negative acceleration

Deceleration: acceleration opposite to the direction of motion/velocity. Always reduces speed

Negative acceleration: acceleration in the negative direction in the chosen coordinate system

Instantaneous acceleration

Acceleration at specific time. Found using average acceleration representative of motion.

if air resistance and friction are negligible, then in a given location all objects fall toward the centre of Earth with the same ___

Constant acceleration, independent of their mass

Free fall

Falling without air resistance or friction, with acceleration due to gravity

A graph of velocity vs. time of a ship coming into a harbor is shown below. (a) Describe the motion of the ship based on the graph. (b)What would a graph of the ship’s acceleration look like?

(a) The ship moves at constant velocity and then begins to decelerate at a constant rate. At some point, its deceleration rate decreases. It maintains this lower deceleration rate until it stops moving.

(b) A graph of acceleration vs. time would show zero acceleration in the first leg, large and constant negative acceleration in the second leg, and constant negative acceleration.

you walk out and back at constant speed on a 100m track in 2.0 minutes. What is. Your displacement?

0 m

you walk out and back at constant speed on a 100m track in 2.0 minutes. What is. Your average velocity?

0 m/s

Which represents your displacement on the 100 m track

B)

Which represents velocity on the 100 m track

C

Which curve represents displacement

A

Which graph represents the acceleration down the 100 m track

C

At what time is acceleration maximum

A