Calculating Car's Acceleration from Rest
Question:
Starting from rest, a car travels 18 meters as it accelerates uniformly for 3.0 seconds. What is the magnitude of the car's acceleration?
Answer:
Acceleration: 4 m/s^2
Explanation:
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In this case, for this uniformly accelerated motion in which the car starts from rest at 0 m/s and travels 18 m in 3.0 s, we can compute the acceleration by using the following equation:
a = 2(x_f - v_0t) / t^2
Whereas the final distance is 18 m, the initial distance is 0 m, the initial velocity is 0 m/s and the time is 3.0 s, that is why the acceleration turns out:
a = 2(18 m - 0 m/s * 3.0 s) / (3.0 s)^2
a = 4 m/s^2
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Final answer: The magnitude of the car's acceleration, starting from rest over a distance of 18 meters in 3.0 seconds, is calculated to be 4.0 m/s^2 using the kinematic equation. Explanation: To find the magnitude of the car's acceleration, we can use the kinematic equation s = ut + 1/2at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time. Starting from rest means that the initial velocity u is 0. So, the equation simplifies to s = 1/2at^2. Given the displacement s is 18 meters and the time t is 3.0 seconds, we can solve for acceleration a as follows: 18 = 1/2a(3.0)^2 36 = 9a a = 4.0 m/s^2 Therefore, the magnitude of the car's acceleration is 4.0 m/s^2.