Question #214613

To stop a car, you require first a certain reaction time to begin braking, during which the car travels at uniform speed, then the car slows down under the constant braking deceleration. Suppose that the total distance moved by your car during these two phases is 186ft when it's initial speed is 50 mi/ h, and 80 ft when it's initial speed is 30 mi/h. What are (a) your reaction time and (b) the magnitude of the deceleration?

Expert's answer

Part 1

"Case 1\\\\\n\\frac{u_1^2}{2a}=x_1+u_1t\\\\\n\nCase 2\\\\\nx_2=u_2t+\\frac{u_2^2}{2a}\\\\\n\\frac{u_2^2}{2a}=x_2-u_2t\\\\\nSo, \\frac{u_1^2}{u_2^2}=\\frac{x_1-u_1t}{x_2-u_2t}\\\\\nu_1^2x_2-u_2u_1^2t= x_1u_2^2-u_1u_2^2t\\\\\nt= \\frac{x_1u_2^2-x_2u_1^2}{u_1^2u_2-u_1u_2^2}\\\\\nt= \\frac{56.693*13.411^2-24.384*22.352^2}{22.352*13.411(22.352-13.411}\\\\\nt=0.741 s"

Part 2

"a= \\frac{u_1^2}{2(x_1-u_1t)}\\\\\na= \\frac{22.352^2}{2(56.693-22.352*0.741)}\\\\\na=6.22 m\/s^2"

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