In Mud buggy driving, people attempt to drive an off-road vehicle over a deep mud puddle. If the buggy stops before the end , it sinks into the mud and needs to be pulled out with a tow truck. A racer is driving his mud buggy in a straight line. when he hits the edge of the mud puddle, he is going 20 m/s. when he gets to the other side of the 25 m wide puddle he has slowed to 5m/s. for each of the kinematics variables determine if they are known or unknown and the known values are:

starting position:
final position:
starting velocity:
final velocity:
acceleration (constant):a
final time (starting time is zero)

To determine the known and unknown variables in this scenario, let's identify the given values:

Known values:
- Starting position: Not specified
- Final position: 25 m (width of the mud puddle)
- Starting velocity: 20 m/s
- Final velocity: 5 m/s
- Acceleration (constant): Not specified
- Final time (starting time is zero): Not specified

Unknown values:
- Starting position
- Acceleration
- Final time

To solve for the unknowns, we need to use the appropriate kinematic equation. In this case, we can use the equation:

v^2 = u^2 + 2as

Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the displacement (change in position)

First, let's find the acceleration (a):

5^2 = 20^2 + 2a(25)
25 = 400 + 50a
50a = -375
a = -7.5 m/s^2

Now that we know the acceleration, we can use another kinematic equation to find the starting position (s):

s = ut + (1/2)at^2

Since the starting time is zero, the equation simplifies to:

s = (1/2)at^2

Substituting the known values:
25 = (1/2)(-7.5)(t^2)
50 = -7.5t^2
t^2 = -50 / -7.5
t^2 = 6.67

Since time cannot be negative in this context, we ignore the negative solution. Therefore, t ≈ √6.67 ≈ 2.58 s (approximated).

Now we can calculate the starting position (s) using the time (t) value:

s = (1/2)(-7.5)(2.58^2)
s ≈ 33.36 m

Therefore, the unknown variables are:
- Starting position ≈ 33.36 m
- Acceleration = -7.5 m/s^2
- Final time ≈ 2.58 s