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Ans: C A car is 210 m from a stop sign and traveling toward the sign at 40m/s At this time, the driver suddenly realizes that she must stop the car. II she applies the brakes after a reaction time of 0.25 < what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign?
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To solve this problem, we need to find the magnitude of the constant acceleration required for the car to come to rest at the stop sign.Given information:- The car is 210 m from the stop sign.- The car is traveling toward the stop sign at 40 m/s.- The driver has a reaction time of 0.25 s before applying the brakes.Step 1: Calculate the distance the car travels during the reaction time.Distance traveled during reaction time = (initial velocity) × (reaction time)Distance traveled during reaction time = (40 m/s) × (0.25 s) = 10 mStep 2: Calculate the remaining distance the car needs to travel to reach the stop sign.Remaining distance = (total distance) - (distance traveled during reaction time)Remaining distance = (210 m) - (10 m) = 200 mStep 3: Use the kinematic equation to find the required acceleration.Final velocity (v_f) = 0 m/s (the car comes to rest)Initial velocity (v_i) = 40 m/sAcceleration (a) =?Time (t) = (remaining distance) / (initial velocity)Time = (200 m) / (40 m/s) = 5 sUsing the kinematic equation: v_f = v_i + 2a(t)0 = 40 + 2a(5)a = -40 / 10 = -4 m/s²Therefore, the magnitude of the constant acceleration required for the car to come to rest at the stop sign is 4 m/s².