A sprinter accelerates uniformly from rest to a speed U m/s in 4 seconds. They then maintain this speed for 16 seconds before decelerating uniformly to rest in 5 seconds. If the total distance covered

The total distance covered in the race is the area under the speed-time graph from $t=0$ to $t=25$ seconds. The total distance is given as $200\, \text{m}$.
The area consists of three parts:

• Triangle from $t=0$ to $t=4$: $\frac{1}{2} \times 4 \times U = 2U$
• Rectangle from $t=4$ to $t=20$: $(20 - 4) \times U = 16U$
• Triangle from $t=20$ to $t=25$: $\frac{1}{2} \times (25 - 20) \times U = \frac{1}{2} \times 5 \times U = 2.5U$ Total distance = $2U + 16U + 2.5U = 20.5U$. Given total distance is $200\, \text{m}$:

$$20.5U = 200$$ $$U = \frac{200}{20.5} = \frac{200}{\frac{41}{2}} = \frac{400}{41}\, \text{m/s}$$