test","extracted_subject":"PHYSICS","extracted_chapter":"MOTION IN A PLANE","extracted_topic":"RELATIVE VELOCITY IN TWO DIMENSIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_68.png?top_left_x=0&top_left_y=679&width=532&height=339&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23c5770136192204b83b2","slug":"a-point-moves-on-the-xy-plane-according-to-the-law","content":"A point moves on the xy plane according to the law x = a sin ωt and y = a(1 – cosωt) where a and ω are positive constants. Find the distance covered in time t₀.","options":[{"_id":"68a41cff7f15af4716ca375b","text":"aωt₀","sequence":0,"isCorrect":true},{"_id":"68a41cff7f15af4716ca375c","text":"\\(\\sqrt{2a^{2} + 2a^{2}\\cos\\omega t_{0}}\\)","sequence":1,"isCorrect":false},{"_id":"68a41cff7f15af4716ca375d","text":"2a (sin ωt₀/2)","sequence":2,"isCorrect":false},{"_id":"68a41cff7f15af4716ca375e","text":"2a (cos ωt₀/2)","sequence":3,"isCorrect":false}],"correct_answer":"aωt₀","explanation":"v_x = aω cos ωt and\n\nv_y = a ω sint ωt\n\nor v = aωcos cot \\(\\widehat{i}\\) + aω sin ωt\\(\\widehat{j}\\) or \\|v\\| = aω\n\ns = \\|v\\|t₀ = aωt₀.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:40:39.155Z","__v":0,"vector_store_id":"0ce4d754-bb6f-485c-bcda-33fd7c70e1ed","updated_at":"2024-08-30T21:40:39.155Z","isStarred":false},"params":{"questionSlug":"a-point-moves-on-the-xy-plane-according-to-the-law"}}]}]]

Question: A point moves on the xy plane according to the law x = a sin ωt and y = a(1 – cosωt) where a and ω a...

Solution