What is the walking speed of the student, from home to the bus stop?

Applications and Skills
Determining instantaneous and average values for velocity, speed
and acceleration
Solving problems using equations of motion for uniform
acceleration
Determining the acceleration of free-fall experimentally
Sketching and interpreting motion graphs
Analysing projectile motion, including the resolution of vertical
and horizontal components of acceleration, velocity and
displacement
Qualitatively describing the effect of fluid resistance on falling
objects or projectiles, including reaching terminal speed

Understandings
Distance and displacement
Speed and velocity
Acceleration
Graphs describing motion
Equations of motion for uniform acceleration
Projectile motion
Fluid resistance and terminal speed

$$ \text{Booklet:}\\ v= u+at\\ s=ut+\frac{1}{2}at^2\\ v^2 = u^2 + 2as\\s=\frac{(v+u)t}{2}\\\text{ }\\s\text{ = displacement (metres)}\\u\text{ = initial velocity (metres per second)}\\v\text{ = final velocity (metres per second)}\\a\text{ = acceleration (metres per second per second )}\\t\text{ = total time (seconds)} $$

Distance and Displacement

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Distance: how far something has travelled without regards to direction.
- M. Fly needs to travel 6m to get to the cheese.
Displacement: not only the distance travelled but also the direction.
- M. Fly needs to travel 6m to the right, to get to the cheese.

Examples:

Find each displacement. Note that the x = 0 coordinate has been placed on the number lines.
A ball starts rolling down a hill from rest with a constant acceleration of . Find the velocity of the ball after 4 seconds. How far has the ball travelled in that time?
- Solution
A cyclist is in a race and 100 metres from the finish he decides to accelerate his speed. The cyclist maintains a constant acceleration of $0.4\text{m/s}^2$. If the cyclist crosses the finish line with a speed of 17m/s, how fast was he cycling when he started to accelerate?
- Solution

Speed and Velocity

Speed: scalar quantity defined as $\frac{\text{distance travelled on journey}}{\text{time taken for journey}}$. The unit for speed is $\bold{ms^{-1}}$.
Velocity: is a vector term and, just as for displacement , a magnitude and direction are required.

Defined as:

$$ v= \frac{\text{displacement of a journey}}{\text{time for a journey}} = \frac{\Delta x}{\Delta t}= \frac{s}{t} $$

Examples:

A runner travels 64.5 meters in the negative x-direction in 31.75 seconds. Find her velocity, and her speed.
A cyclist travels 16 km in 70 minutes. Calculate, in $\bold{ms^{-1}}$, the speed of the cyclist.
The speed of light in a vacuum is $3.0*10^*8ms^{-1}$. A star is 22 light years from Earth (1 light year is the distance travelled by light in one year). Calculate the distance of the star from Earth in kilometres.

Acceleration

Being the rate of change of velocity, it can also be described as the derivative of a velocity/time curve.