a) 893 N
b) 8.5 m/s
c) 3816 W
d) 69780 J
e) 8030 W
Explanation:
a)
The net force acting on Bolt during the acceleration phase can be written using Newton's second law of motion:

where
m is Bolt's mass
a is the acceleration
In the first 0.890 s of motion, we have
m = 94.0 kg (Bolt's mass)
 (acceleration)
 (acceleration)
So, the net force is

And according to Newton's third law of motion, this force is equivalent to the force exerted by Bolt on the ground (because they form an action-reaction pair).
b)
Since Bolt's motion is a uniformly accelerated motion, we can find his final speed by using the following suvat equation:

where
v is the  final speed
u is the initial speed
a is the acceleration
t is the time
In the first phase of Bolt's race we have:
u = 0 m/s (he starts from rest)
 (acceleration)
 (acceleration)
t = 0.890 s (duration of the first phase)
Solving for v,

c)
First of all, we can calculate the work done by Bolt to accelerate to a speed of 
v = 8.5 m/s
According to the work-energy theorem, the work done is equal to the change in kinetic energy, so

where
m = 94.0 kg is Bolt's mass
v = 8.5 m/s is Bolt's final speed after the first phase
 is the initial kinetic energy
 is the initial kinetic energy
So the work done is

The power expended is given by

where
t = 0.890 s is the time elapsed
Substituting,

d)
First of all, we need to find what is the average force exerted by Bolt during the remaining 8.69 s of motion.
In the first 0.890 s, the force exerted was

We know that the average force for the whole race is

Which can be rewritten as

And solving for  , we find the average force exerted by Bolt on the ground during the second phase:
, we find the average force exerted by Bolt on the ground during the second phase:

The net force exerted by Bolt during the second phase can be written as
 (1)
 (1)
where D is the air drag.
The net force can also be rewritten as

where
 is the acceleration in the second phase, with
 is the acceleration in the second phase, with
u = 8.5 m/s is the initial speed
v = 12.4 m/s is the final speed
t = 8.69 t is the time elapsed
Substituting,

So we can now find the average drag force from (1):

So the increase in Bolt's internal energy is just equal to the work done by the drag force, so:

where
d is Bolt's displacement in the second part, which can be found by using suvat equation:

And so,

e)
The power that Bolt must expend just to voercome the drag force is given by

where
 is the increase in internal energy due to the air drag
 is the increase in internal energy due to the air drag
t is the time elapsed
Here we have:

t = 8.69 s is the time elapsed
Substituting,

And we see that it is about twice larger than the power calculated in part c.