Car Acceleration: Solving for Uniform Acceleration Rate
What kind of problem involves a car accelerating uniformly from rest to a certain speed after traveling a specific distance?
Is it possible to calculate the acceleration of the car based on the given information? If so, how can we determine the acceleration rate?
Answer:
Yes, it is possible to calculate the acceleration of the car based on the given data. The acceleration rate can be determined using one of the equations of motion related to distance, speed, and acceleration.
When a car starts from rest and accelerates uniformly to reach a certain speed after covering a specific distance, we can use physics principles, specifically kinematics, to solve for the acceleration rate of the car. The equation that relates final velocity, initial velocity, acceleration, and distance is essential in solving such problems.
Calculating the Acceleration Rate:
Given that the car accelerated from rest to a speed of 25 m/s after traveling 75m, we can use the equation: final velocity² = initial velocity² + 2 * acceleration * distance. Since the car started from rest, the initial velocity is 0 m/s.
Plugging in the values, we have: 25² = 0 + 2 * acceleration * 75. Simplifying the equation gives us an acceleration rate of 4.17 m/s². Therefore, the car accelerated uniformly at a rate of 4.17 m/s².