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?

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.<br /><br />Given information:<br />- The car is 210 m from the stop sign.<br />- The car is traveling toward the stop sign at 40 m/s.<br />- The driver has a reaction time of 0.25 s before applying the brakes.<br /><br />Step 1: Calculate the distance the car travels during the reaction time.<br />Distance traveled during reaction time = (initial velocity) × (reaction time)<br />Distance traveled during reaction time = (40 m/s) × (0.25 s) = 10 m<br /><br />Step 2: Calculate the remaining distance the car needs to travel to reach the stop sign.<br />Remaining distance = (total distance) - (distance traveled during reaction time)<br />Remaining distance = (210 m) - (10 m) = 200 m<br /><br />Step 3: Use the kinematic equation to find the required acceleration.<br />Final velocity (v_f) = 0 m/s (the car comes to rest)<br />Initial velocity (v_i) = 40 m/s<br />Acceleration (a) =?<br />Time (t) = (remaining distance) / (initial velocity)<br />Time = (200 m) / (40 m/s) = 5 s<br /><br />Using the kinematic equation: v_f = v_i + 2a(t)<br />0 = 40 + 2a(5)<br />a = -40 / 10 = -4 m/s²<br /><br />Therefore, the magnitude of the constant acceleration required for the car to come to rest at the stop sign is 4 m/s².