{"id":31356,"date":"2025-06-21T23:27:17","date_gmt":"2025-06-21T23:27:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=31356"},"modified":"2025-06-21T23:27:21","modified_gmt":"2025-06-21T23:27:21","slug":"a-driver-has-a-reaction-time-of-0-50-s-and-the-maximum-deceleration-of-her-car-is-6-0-m-s-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-driver-has-a-reaction-time-of-0-50-s-and-the-maximum-deceleration-of-her-car-is-6-0-m-s-2\/","title":{"rendered":"A driver has a reaction time of 0.50 s , and the maximum deceleration of her car is 6.0 m\/ s 2"},"content":{"rendered":"\n

A driver has a reaction time of 0.50 s , and the maximum deceleration of her car is 6.0 m\/ s 2 . She is driving at 20 m\/s when suddenly she sees an obstacle in the road 50 m in front of her. what is the distance she passes after noticing the obstacle before fully stopping?<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer: 53.3 meters<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To find the total distance the driver travels after noticing the obstacle before coming to a complete stop, we divide the motion into two parts:<\/p>\n\n\n\n

\n\n\n\n

Part 1: Distance traveled during reaction time<\/strong><\/p>\n\n\n\n

During the reaction time<\/strong> of 0.50 seconds, the driver continues to move at the same initial speed of 20 m\/s, since no braking has occurred yet.<\/p>\n\n\n\n

Using the formula for constant velocity: d1=v\u22c5td_1 = v \\cdot t d1=20\u2009m\/s\u22c50.50\u2009s=10\u2009metersd_1 = 20 \\, \\text{m\/s} \\cdot 0.50 \\, \\text{s} = 10 \\, \\text{meters}<\/p>\n\n\n\n

\n\n\n\n

Part 2: Distance traveled while decelerating<\/strong><\/p>\n\n\n\n

Once the driver reacts, she begins to decelerate<\/strong> at 6.0 m\/s\u00b2 until the car stops. We calculate the braking distance using the kinematic equation: v2=u2+2adv^2 = u^2 + 2ad<\/p>\n\n\n\n

Here:<\/p>\n\n\n\n

    \n
  • Final velocity v=0\u2009m\/sv = 0 \\, \\text{m\/s}<\/li>\n\n\n\n
  • Initial velocity u=20\u2009m\/su = 20 \\, \\text{m\/s}<\/li>\n\n\n\n
  • Acceleration a=\u22126.0\u2009m\/s2a = -6.0 \\, \\text{m\/s}^2 (deceleration)<\/li>\n<\/ul>\n\n\n\n

    Solving for dd: 0=(20)2+2(\u22126.0)d0 = (20)^2 + 2(-6.0)d 0=400\u221212d0 = 400 – 12d 12d=400\u21d2d=40012\u224833.3\u2009meters12d = 400 \\Rightarrow d = \\frac{400}{12} \\approx 33.3 \\, \\text{meters}<\/p>\n\n\n\n

    \n\n\n\n

    Total stopping distance:<\/strong> Total distance=d1+d2=10+33.3=43.3\u2009meters\\text{Total distance} = d_1 + d_2 = 10 + 33.3 = 43.3 \\, \\text{meters}<\/p>\n\n\n\n

    \n\n\n\n

    Comparison with obstacle distance:<\/strong><\/p>\n\n\n\n

    The obstacle is 50 meters away, and the driver stops after 43.3 meters. This means she does not hit the obstacle<\/strong> and stops safely with about 6.7 meters<\/strong> to spare.<\/p>\n\n\n\n

    This problem illustrates how reaction time and deceleration rate are critical in stopping distances. Even a small delay in reaction can significantly increase the total distance traveled before stopping.<\/p>\n","protected":false},"excerpt":{"rendered":"

    A driver has a reaction time of 0.50 s , and the maximum deceleration of her car is 6.0 m\/ s 2 . She is driving at 20 m\/s when suddenly she sees an obstacle in the road 50 m in front of her. what is the distance she passes after noticing the obstacle before […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-31356","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=31356"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31356\/revisions"}],"predecessor-version":[{"id":31357,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31356\/revisions\/31357"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=31356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=31356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=31356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}