UPSC Exam > UPSC Questions > A car of mass M accelerates starting from res...
Start Learning for Free
A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by?
Most Upvoted Answer
A car of mass M accelerates starting from rest .velocity of the car is...
Position of the Car as a Function of Time
Position as a Function of Time Formula:
- The position of the car as a function of time can be determined by integrating the velocity equation with respect to time.
- Given that velocity v = (Pt/M)^0.5, the position x can be found by integrating v with respect to time.
Integration Process:
- Integrate v = (Pt/M)^0.5 with respect to time to find x(t).
- The integral of (Pt/M)^0.5 with respect to time is (2P/M)^0.5 * t^(3/2) / 3.
Final Position Equation:
- Therefore, the position x of the car as a function of time t is x(t) = (2P/M)^0.5 * t^(3/2) / 3 + C, where C is the constant of integration.
Explanation:
- As the car accelerates from rest, the position of the car increases with time following the equation x(t) = (2P/M)^0.5 * t^(3/2) / 3.
- This equation shows that the position of the car is directly proportional to the cube root of time, indicating a non-linear relationship between position and time.
- The constant power supplied by the engine P influences the rate at which the car's position changes over time, with higher power leading to faster acceleration and greater displacement.
In conclusion, the position of the car as a function of time can be determined by integrating the velocity equation and considering the constant power supplied by the engine. This mathematical relationship provides insights into the motion of the car as it accelerates from rest.
Position as a Function of Time Formula:
- The position of the car as a function of time can be determined by integrating the velocity equation with respect to time.
- Given that velocity v = (Pt/M)^0.5, the position x can be found by integrating v with respect to time.
Integration Process:
- Integrate v = (Pt/M)^0.5 with respect to time to find x(t).
- The integral of (Pt/M)^0.5 with respect to time is (2P/M)^0.5 * t^(3/2) / 3.
Final Position Equation:
- Therefore, the position x of the car as a function of time t is x(t) = (2P/M)^0.5 * t^(3/2) / 3 + C, where C is the constant of integration.
Explanation:
- As the car accelerates from rest, the position of the car increases with time following the equation x(t) = (2P/M)^0.5 * t^(3/2) / 3.
- This equation shows that the position of the car is directly proportional to the cube root of time, indicating a non-linear relationship between position and time.
- The constant power supplied by the engine P influences the rate at which the car's position changes over time, with higher power leading to faster acceleration and greater displacement.
In conclusion, the position of the car as a function of time can be determined by integrating the velocity equation and considering the constant power supplied by the engine. This mathematical relationship provides insights into the motion of the car as it accelerates from rest.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by?
Question Description
A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by?.
A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by?.
Solutions for A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? defined & explained in the simplest way possible. Besides giving the explanation of
A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by?, a detailed solution for A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? has been provided alongside types of A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? theory, EduRev gives you an
ample number of questions to practice A car of mass M accelerates starting from rest .velocity of the car is given by v=(Pt/M)½. where P is the constant power supplied by the engine . the position of the car as a function of time is given by? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup