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------------------------------------------------ Calculate the force (in N) needed to bring an 891 kg car to rest from a speed of 81 km/h over a distance of 103 m.

The force required to bring the car to rest can be calculated using Newton's second law of motion and the kinematic equation. First, convert the speed to m/s, calculate the deceleration needed to stop the car in the given distance, and multiply it by the car's mass to find the force.

Explanation:

The problem you're dealing with is a straightforward application of Newton's second law of motion (F=ma), combined with a kinematic equation to solve for acceleration. First, we need to convert your speed from km/h to m/s. Your speed in m/s is 81 km/h divided by 3.6, which equals to approximately 22.5 m/s.

Now, the next step is to find acceleration using the equation v_f^2 = v_i^2 + 2as where v_f is the final velocity (0 m/s since it comes to rest), v_i is the initial velocity (22.5 m/s), 'a' is the acceleration, and 's' is the distance (103 m). Solving this for 'a', we get acceleration as approximately -2.45 m/s² (negative since it's deceleration).

Finally, we apply Newton's second law: F = ma. Substituting the values, we get force as approximately -2185 N (negative showing the force direction is opposite to motion).

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