Question

in coming to a stop, a car leaves skid marks on the highway 250 m long. assuming an acceleration of - 12.00 m/s², estimate the speed of the car just before braking.
round to the first decimal place.
answer
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Explanation:

Step1: Identify the kinematic equation

We use the kinematic equation \(v^{2}=v_{0}^{2}+2ax\). Since the car comes to a stop, \(v = 0\). The equation becomes \(0 = v_{0}^{2}+2ax\), and we can solve for \(v_{0}\): \(v_{0}=\sqrt{- 2ax}\).

Step2: Substitute the values

Given \(a=-12.00\ m/s^{2}\) and \(x = 250\ m\). Substitute into the formula: \(v_{0}=\sqrt{-2\times(- 12.00)\times250}\).
First, calculate \(-2\times(-12.00)\times250=6000\). Then \(v_{0}=\sqrt{6000}\approx77.5\ m/s\).

Answer:

\(77.5\ m/s\)