The final velocity vf of an object is given by the formula vf=vi + at, where vi is the initial velocity, a is the acceleration, and t is the time. a. solve the formula for t. justify each step.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve the formula ( v_f = v_i + at ) for ( t ), we want to isolate ( t ) on one side of the equation. Here\u2019s a step-by-step breakdown:<\/p>\n\n\n\n The correct answer is: <\/strong><\/mark><\/p>\n\n\n\n [ To isolate the term containing ( t ), subtract ( v_i ) from both sides of the equation: Next, we need to get ( t ) by itself. Since ( a ) is multiplied by ( t ), we divide both sides by ( a ) (assuming ( a \\neq 0 )): The final expression ( t = \\frac{v_f – v_i}{a} ) shows how time ( t ) depends on the change in velocity (( v_f – v_i )) and acceleration ( a ).<\/p>\n\n\n\n This formula is particularly useful in physics, especially in kinematics, where it describes how an object accelerates over time. The variables represent fundamental concepts in motion: ( v_f ) (final velocity) indicates how fast the object is moving at a certain point; ( v_i ) (initial velocity) is the speed at which the object started; and ( a ) (acceleration) represents the rate at which the object speeds up or slows down.<\/p>\n\n\n\n By manipulating the equation, we effectively express time ( t ) as the ratio of the change in velocity to acceleration. This ratio provides insight into how long it takes for an object to reach a certain speed given a specific acceleration. Understanding this relationship is critical in various applications, from designing vehicles to analyzing sports performance, as it helps predict how quickly an object can accelerate to its desired speed.<\/p>\n","protected":false},"excerpt":{"rendered":" The final velocity vf of an object is given by the formula vf=vi + at, where vi is the initial velocity, a is the acceleration, and t is the time. a. solve the formula for t. justify each step. The Correct Answer and Explanation is : To solve the formula ( v_f = v_i + […]<\/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-148663","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148663","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=148663"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148663\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=148663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=148663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=148663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Start with the original equation<\/h3>\n\n\n\n
v_f = v_i + at
]
This equation states that the final velocity ( v_f ) is equal to the initial velocity ( v_i ) plus the product of acceleration ( a ) and time ( t ).<\/p>\n\n\n\nStep 2: Subtract ( v_i ) from both sides<\/h3>\n\n\n\n
[
v_f – v_i = at
]
This step simplifies the equation by moving ( v_i ) away from the right side.<\/p>\n\n\n\nStep 3: Divide both sides by ( a )<\/h3>\n\n\n\n
[
t = \\frac{v_f – v_i}{a}
]
This rearrangement reveals ( t ) in terms of ( v_f ), ( v_i ), and ( a ).<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n