Answer :
Final answer:
To find the distance a car travels when accelerating from rest, use the equation for acceleration. These examples involve calculating the distance travelled during acceleration on a freeway and the time taken to travel up a ramp while accelerating.
Explanation:
The subject of this question is the calculation of distance and velocity during Acceleration while merging onto an interstate (freeway). In the first example, a car accelerates from rest at a rate of 2.40 m/s² for 12.0 s. To find out how far the car traveled within this time you would use the equation for acceleration: distance = initial velocity * time + 0.5 * acceleration * time². Since the car is starting from rest, initial velocity is zero, and the equation simplifies to distance = 0.5 * acceleration * time². Substitute the given values into the equation: distance = 0.5 * 2.40 m/s² * (12.0 s)². Following the steps will provide the answer to the question. In the second given example, a car merges into freeway traffic on a 200m ramp. It has an initial velocity of 10.0m/s and accelerates at 2.00m/s². To solve for the duration of the car's travel up the ramp, you can use the equation: time = (final_velocity - initial_velocity)/acceleration. Note that the final velocity can be found from the equation of motion: final_velocity = sqrt(initial_velocity² + 2*acceleration*distance).
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