Final answer:
The overtaking time for a car accelerating from 85 km/h to 115 km/h while passing a 30-m-long truck is approximately 3.6 seconds, calculated using the relative velocity of the car to the truck.
Step-by-step explanation:
The question deals with the motion of a car overtaking a truck and asks for the duration of the overtaking process given that the truck is 30 meters long and the car accelerates from an initial velocity equal to the truck's to a final velocity after overtaking.
First, we need to calculate the relative velocity of the car with respect to the truck during the overtaking process. Let's assume the car accelerates uniformly from 85 km/h to 115 km/h. Since the truck's velocity is constant at 85 km/h, the relative velocity between the car and the truck is the difference in their speeds when the car is overtaking. This gives us a relative velocity of 115 km/h - 85 km/h = 30 km/h (which is 8.33 m/s after converting from km/h to m/s).
Once we have the relative velocity, we can use the formula distance = velocity × time to find the overtaking time. The distance to be covered is the length of the truck, which is 30 meters, so time can be calculated as: time = distance / relative velocity. Plugging in the known values, we get time = 30 m / 8.33 m/s, which gives us approximately 3.6 seconds.