Question

When running a 100 meter race Sergio reaches his maximum speed when he is 40 meters from the starting line, and 6 seconds have elapsed since the start of the race. Sergio continues at this max speed for the rest of the race and is 85 meters from the starting line 11 seconds after the start of the race. What is Sergio's max speed? meters per second Suppose Sergio runs for an additional 3 seconds after reaching his max speed... How far will Sergio travel during those 3 seconds? meters What is Sergio's distance from the starting line 9 seconds after the start of the race? meters What is Sergio's distance from the starting line 7.5 seconds after the start of the race? meters

Answer 1

13.32 m/s

39.96 m

79.96 m

59.98 m

Step-by-step explanation:

`s=ut+(1)/(2)at^2\\\Rightarrow 40=0* 6+(1)/(2)* a* 6^2\\\Rightarrow a=(40* 2)/(6^2)\\\Rightarrow a=2.22\ m/s^2`

`v=u+at\\\Rightarrow v=0+2.22* 6\\\Rightarrow v=13.32\ m/s`

Maximum speed of Sergio is 13.32 m/s

If Sergio runs for 3 seconds after reaching his maximum speed

Distance = Speed × Time

`\text{Distance}=13.32* 3=39.96\ m`

In the three second Sergio will cover 39.96 m

In 6 seconds he covers 40 m. In the extra 3 seconds he covers 39.96 m

So, total distance covered in 9 seconds is 40+39.96 = 79.96 m

Distance covered in 6 seconds is 40 m.

`\text{Distance}=13.32* (7.5-6)=19.98\ m`

In 1.5 seconds he will cover 19.98 m

So, in 7.5 seconds he will cover 40+19.98 = 59.98 m