{"id":87535,"date":"2025-06-01T06:47:09","date_gmt":"2025-06-01T06:47:09","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87535"},"modified":"2025-06-01T06:47:09","modified_gmt":"2025-06-01T06:47:09","slug":"an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/","title":{"rendered":"An object is moving with uniform acceleration a. Its initial velocity"},"content":{"rendered":"

An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v = u + at. The velocity (along y-axis) time (along x-axis) graph shall be a straight line<\/p>\n

[amp_mcq option1=”passing through origin” option2=”with x-intercept u” option3=”with y-intercept u” option4=”with slope u” correct=”option3″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC NDA-1 – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe given equation of motion is v = u + at. We are asked about the velocity (v) vs. time (t) graph. This equation is in the form of a linear equation, y = mx + c, where v corresponds to y, t corresponds to x, ‘a’ (uniform acceleration) is the slope (m), and ‘u’ (initial velocity) is the y-intercept (c). The y-intercept is the value of y when x=0. In this case, it is the value of velocity (v) when time (t) is zero, which is the initial velocity ‘u’. Therefore, the graph is a straight line with a y-intercept equal to u.
\n<\/section>\n
\n– The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration.
\n– In a linear equation y = mx + c, ‘c’ is the y-intercept and ‘m’ is the slope.
\n– On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.
\n<\/section>\n
\nThe slope of the velocity-time graph represents the acceleration. Since the acceleration ‘a’ is uniform (constant), the graph is a straight line. The graph passes through the origin only if the initial velocity u is zero. The x-intercept would be the time when velocity is zero, which is t = -u\/a (if applicable and physically meaningful).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v = u + at. The velocity (along y-axis) time (along x-axis) graph shall be a straight line [amp_mcq option1=”passing through origin” option2=”with x-intercept u” option3=”with y-intercept u” … <\/p>\n

Detailed SolutionAn object is moving with uniform acceleration a. Its initial velocity<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1114,1129,1128],"class_list":["post-87535","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1114","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nAn object is moving with uniform acceleration a. Its initial velocity<\/title>\n<meta name=\"description\" content=\"The given equation of motion is v = u + at. We are asked about the velocity (v) vs. time (t) graph. This equation is in the form of a linear equation, y = mx + c, where v corresponds to y, t corresponds to x, 'a' (uniform acceleration) is the slope (m), and 'u' (initial velocity) is the y-intercept (c). The y-intercept is the value of y when x=0. In this case, it is the value of velocity (v) when time (t) is zero, which is the initial velocity 'u'. Therefore, the graph is a straight line with a y-intercept equal to u. - The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration. - In a linear equation y = mx + c, 'c' is the y-intercept and 'm' is the slope. - On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An object is moving with uniform acceleration a. Its initial velocity\" \/>\n<meta property=\"og:description\" content=\"The given equation of motion is v = u + at. We are asked about the velocity (v) vs. time (t) graph. This equation is in the form of a linear equation, y = mx + c, where v corresponds to y, t corresponds to x, 'a' (uniform acceleration) is the slope (m), and 'u' (initial velocity) is the y-intercept (c). The y-intercept is the value of y when x=0. In this case, it is the value of velocity (v) when time (t) is zero, which is the initial velocity 'u'. Therefore, the graph is a straight line with a y-intercept equal to u. - The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration. - In a linear equation y = mx + c, 'c' is the y-intercept and 'm' is the slope. - On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:47:09+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"An object is moving with uniform acceleration a. 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Therefore, the graph is a straight line with a y-intercept equal to u. - The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration. - In a linear equation y = mx + c, 'c' is the y-intercept and 'm' is the slope. - On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/","og_locale":"en_US","og_type":"article","og_title":"An object is moving with uniform acceleration a. Its initial velocity","og_description":"The given equation of motion is v = u + at. We are asked about the velocity (v) vs. time (t) graph. 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Therefore, the graph is a straight line with a y-intercept equal to u. - The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration. - In a linear equation y = mx + c, 'c' is the y-intercept and 'm' is the slope. - On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:47:09+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/","name":"An object is moving with uniform acceleration a. 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Therefore, the graph is a straight line with a y-intercept equal to u. - The equation v = u + at is a linear relationship between velocity (v) and time (t) for uniform acceleration. - In a linear equation y = mx + c, 'c' is the y-intercept and 'm' is the slope. - On a velocity-time graph, the y-axis represents velocity and the x-axis represents time.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-moving-with-uniform-acceleration-a-its-initial-velocity\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-1","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-1\/"},{"@type":"ListItem","position":3,"name":"An object is moving with uniform acceleration a. 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