Final answer:
To calculate the maximum acceleration of a car heading up a slope, consider the forces acting on the car and use trigonometry and Newton's second law to calculate the acceleration for each road condition.
Step-by-step explanation:
To calculate the maximum acceleration of a car heading up a slope, we need to consider the forces acting on the car. On a slope, the gravitational force can be divided into two components: the force parallel to the slope, which contributes to acceleration, and the force perpendicular to the slope, which is counteracted by the normal force. We can use trigonometry to find the force parallel to the slope:
Force parallel to the slope = Force of gravity * sine(angle)
Once we have the force parallel to the slope, we can use Newton's second law (F = m * a) to find the acceleration:
Acceleration = Force parallel to the slope / mass
Repeat this process for each road condition (dry concrete, wet concrete, and ice) using the given coefficients of friction to calculate the maximum acceleration in each case.