{"id":205784,"date":"2025-03-25T16:42:48","date_gmt":"2025-03-25T16:42:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205784"},"modified":"2025-03-25T16:42:51","modified_gmt":"2025-03-25T16:42:51","slug":"motion-in-two-dimensions-name-mech-hw-21-some-students-used-two-straight-segments-and-two-half-circles-to-make-a-track-for-a-toy-car","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/motion-in-two-dimensions-name-mech-hw-21-some-students-used-two-straight-segments-and-two-half-circles-to-make-a-track-for-a-toy-car\/","title":{"rendered":"Motion in two dimensions Name Mech HW-21 Some students used two straight segments and two half circles to make a track for a toy car"},"content":{"rendered":"\n
Motion in two dimensions Name Mech HW-21 Some students used two straight segments and two half circles to make a track for a toy car, shown in the scale diagram at right. Each box on the diagram is 5 cm on a side. The car moves clockwise around the track at constant speed. It takes the car 8 s to go around the track once. a. Determine the speed of the car. Show your work. B 1 box = 5 cm b. Consider the interval that begins when the car passes point A and ends when the car passes point B (halfway around the track). i. On the diagram at right, draw an arrow to represent the direction of Direction of the average velocity over this interval. Explain your reasoning. from A to B avg ya ii. Determine the magnitude of the average velocity of the car over this interval. Show your work. Direction of a iii. On the diagram at right, draw an arrow to represent the direction of the average acceleration over this interval. Explain your reasoning. from A to B iv. Determine the magnitude of the average acceleration of the car over this interval. Show your work.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Solution and Explanation<\/strong><\/h3>\n\n\n\n
(a) Determining the Speed of the Car<\/strong><\/h4>\n\n\n\n
To find the speed of the car, we first determine the total distance it travels in one complete lap.<\/p>\n\n\n\n
\n
Measure the Track Dimensions:<\/strong>\n
\n
The track consists of two straight segments and two half circles.<\/li>\n\n\n\n
Each box in the diagram represents 5 cm<\/strong>.<\/li>\n\n\n\n
From the diagram, each straight segment is 20 cm<\/strong> long.<\/li>\n\n\n\n
The two half-circles together form a full circle with a diameter of 10 cm<\/strong>, giving a circumference of: C=\u03c0d=\u03c0(10\u00a0cm)=31.4\u00a0cmC = \\pi d = \\pi (10 \\text{ cm}) = 31.4 \\text{ cm}<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Total Distance:<\/strong>\n
\n
The straight sections together contribute 40 cm<\/strong>.<\/li>\n\n\n\n
The circular sections contribute 31.4 cm<\/strong>.<\/li>\n\n\n\n
So, the total track length is: 40+31.4=71.4\u00a0cm40 + 31.4 = 71.4 \\text{ cm}<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Find the Speed:<\/strong>\n
\n
Given that the car takes 8 seconds<\/strong> to complete one lap: v=Total\u00a0DistanceTime=71.48=8.93\u00a0cm\/sv = \\frac{\\text{Total Distance}}{\\text{Time}} = \\frac{71.4}{8} = 8.93 \\text{ cm\/s}<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
(b) Motion from A to B<\/strong><\/h4>\n\n\n\n
Since the car moves at constant speed but changes direction, we analyze velocity and acceleration.<\/p>\n\n\n\n
(i) Direction of the Average Velocity<\/strong><\/h5>\n\n\n\n
\n
The car moves halfway around the track<\/strong>, from A to B.<\/li>\n\n\n\n
The average velocity is the displacement divided by time.<\/li>\n\n\n\n
Since A and B are opposite points on the track, the displacement vector points directly across the track, forming a straight line<\/strong>.<\/li>\n\n\n\n
On the diagram, the arrow should point directly from A to B<\/strong>, cutting through the track\u2019s center.<\/li>\n<\/ul>\n\n\n\n
(ii) Magnitude of the Average Velocity<\/strong><\/h5>\n\n\n\n
\n
The displacement is simply the diameter of the track<\/strong>, which is 10 cm<\/strong>.<\/li>\n\n\n\n
The time to travel from A to B is half the total time<\/strong>: t=82=4\u00a0st = \\frac{8}{2} = 4 \\text{ s}<\/li>\n\n\n\n
The average velocity magnitude is: vavg=DisplacementTime=104=2.5\u00a0cm\/sv_{\\text{avg}} = \\frac{\\text{Displacement}}{\\text{Time}} = \\frac{10}{4} = 2.5 \\text{ cm\/s}<\/li>\n<\/ul>\n\n\n\n
(iii) Direction of the Average Acceleration<\/strong><\/h5>\n\n\n\n
\n
Acceleration depends on velocity change.<\/li>\n\n\n\n
The velocity at A and B are perpendicular to each other.<\/li>\n\n\n\n
The change in velocity points toward the track\u2019s center<\/strong>.<\/li>\n\n\n\n
The average acceleration arrow should be drawn from the midpoint of A to B, pointing toward the center of the track<\/strong>.<\/li>\n<\/ul>\n\n\n\n
(iv) Magnitude of the Average Acceleration<\/strong><\/h5>\n\n\n\n
Thus, the average acceleration has a magnitude of 3.16 cm\/s\u00b2<\/strong> and points toward the center of the track.<\/p>\n\n\n\n
Here’s the scale diagram of the toy car track, including the velocity and acceleration directions. Let me know if you need any modifications!<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Motion in two dimensions Name Mech HW-21 Some students used two straight segments and two half circles to make a track for a toy car, shown in the scale diagram at right. Each box on the diagram is 5 cm on a side. The car moves clockwise around the track at constant speed. It takes […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-205784","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=205784"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205784\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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