To determine the forces acting on the vehicle as it turns on a flat road, we can focus on the relationship between centripetal force and friction. The frictional force provides the necessary centripetal force to keep the vehicle on the curved path. Since the car is turning on a flat road, the friction must be static to prevent the car from sliding.

We can calculate the maximum speed at which the car can make the turn without sliding. The formula for the maximum speed $v_{\text{max}}$ that the car can achieve without sliding is:

$v_{\text{max}} = \sqrt{\mu_s \cdot g \cdot r}$

Where:

• $\mu_s = 0.2$ is the coefficient of static friction,
• $g = 9.81 \, \text{m/s}^2$ is the acceleration due to gravity,
• $r = 79 \, \text{m}$ is the radius of the turn.

Step-by-step calculation:

1. Substitute the known values into the equation: $v_{\text{max}} = \sqrt{0.2 \cdot 9.81 \, \text{m/s}^2 \cdot 79 \, \text{m}}$

2. Simplify the expression: $v_{\text{max}} = \sqrt{0.2 \cdot 775.59 \, \text{m}^2/\text{s}^2} = \sqrt{155.118 \, \text{m}^2/\text{s}^2}$

3. Calculate $v_{\text{max}}$: $v_{\text{max}} \approx 12.45 \, \text{m/s}$

Thus, the maximum speed the vehicle can achieve without sliding is approximately 12.45 m/s.

Let me know if you need more details or have further questions!

Here are 5 relative questions to consider:

1. How does the radius of curvature affect the turning speed of the car?
2. What would happen if the coefficient of friction were lower?
3. Can you calculate the required friction coefficient for a higher turning speed?
4. How does kinetic friction affect the scenario if the car begins to skid?
5. What other forces are acting on the car while it makes the turn?

Tip: Increasing the frictional force, for example by driving on a rougher surface, would allow the car to make sharper turns at higher speeds!