**Answer:**

a) The acceleration of Usain Bolt was 2.98 m/s².

His maximum speed was (v = 2.98 m/s² · 3.00 s) 8.94 m/s.

b) The acceleration was 3.21 m/s² and the maximum speed was 9.63 m/s

**Explanation:**

The equation for the position of Bolt during the first 3 s is as follows:

x = x0 + 1/2 · a · t²

Where:

x = position at time t

a = acceleration

t = time

x0 = initial position

After that time, the position is:

x = x0 + v · t

Where "v" is the velocity

During the acceleration, the velocity is:

v = a · t

The maximum speed reached by Bolt is then:

v = a · 3.00 s

The distance traveled during the first 3 seconds is:

x = x0 + 1/2 · a · t² (x0 = 0)

x = 1/2 · a · (3.00 s)²

x = 4.50 s² · a

Then, in the equation of the position after the first 3 s, we can replace the initial position for the position traveled during the first 3 s and the velocity for the velocity reached in those 3 s.

x = x0 + v · t

x0 = 4.50 s² · a

v = a · 3.00 s

Then:

x = 4.50 s² · a + 3.00 s · a ·t

At t = 9.69 s, x = 100 m. Then:

100 m = 4.50 s² · a + 3.00 s · a · 9.69 s

100 m = 33.6 s² · a

100 m / 33.6 s² = a

a = 2.98 m/s²

The acceleration of Usain Bolt was 2.98 m/s².

His maximum speed was (v = 2.98 m/s² · 3.00 s) 8.94 m/s.

b) The calculations are the same only that in the final step we have to use x = 200 m instead of 100 m and t = 19.30 s instead of 9.69 s:

200 m = 4.50 s² · a + 3.00 s · a · 19.30 s

200 m = 62.4 s² · a

200 m / 62.4 s² = a

a = 3.21 m/s²

v = 3.21 m/s² · 3.00 s = 9.63 m/s

The acceleration was 3.21 m/s² and the maximum speed was 9.63 m/s