1) [tex]3.54 m/s^2[/tex]
The average acceleration of the sprinter can be found by using the following SUVAT equation:
[tex]v^2-u^2=2ad[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
d is the distance covered
In this problem,
u = 0 (the sprinter starts from rest)
v = 11.9 m/s
d = 20.0 m
Solving for a, we find the acceleration:
[tex]a=\frac{v^2-u^2}{2d}=\frac{(11.9)^2}{2(20)}=3.54 m/s^2[/tex]
2) 3.36 s
We can find the time needed to reach this speed by using the SUVAT equation:
[tex]v=u+at[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
Here we have
u = 0
v = 11.9 m/s
a = 3.54 m/s^2
Solving for t, we find the time:
[tex]t=\frac{v-u}{a}=\frac{11.9}{3.54}=3.36 s[/tex]
