Mr Tan rides his motorcycle to a coffee shop for breakfast.
He starts from rest and accelerates at a constant rate to a speed of 20 m/s in 15 seconds.
He then travels at this constant speed of 20 m/s for the next 20 seconds before coming to rest in the next 10 seconds.

1. Identify the key points on the speed-time graph from the description.

Mr Tan starts from rest, so the graph starts at $(0,0)$.

He reaches $20\text{ m/s}$ after $15\text{ s}$, giving the point $(15,20)$.

He then travels at $20\text{ m/s}$ for the next $20\text{ s}$, so the time is $15+20=35\text{ s}$, giving $(35,20)$.

He comes to rest in the next $10\text{ s}$, so the final time is $35+10=45\text{ s}$, giving $(45,0)$.

2. Draw the speed-time graph using straight line segments.

Draw straight line segments:

• from $(0,0)$ to $(15,20)$ for constant acceleration,
• from $(15,20)$ to $(35,20)$ for constant speed,
• from $(35,20)$ to $(45,0)$ for constant deceleration.

1. Calculate the acceleration from rest to $20\text{ m/s}$ in $15$ seconds.

Acceleration
$=\frac{\text{change in speed}}{\text{time taken}}=\frac{20-0}{15}=\frac{4}{3}\text{ m/s}^2.$

1. Find the total distance travelled from the area under the speed-time graph.

Distance travelled
$= \frac{1}{2}(15)(20) + (20)(20) + \frac{1}{2}(10)(20)$
$=150+400+100=650\text{ m}$

2. Divide the total distance by the total time to calculate the average speed.

Total time $=15+20+10=45\text{ s}$

Average speed
$=\frac{\text{total distance}}{\text{total time}}$
$=\frac{650}{45}=14.444\ldots$