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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?
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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.
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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?
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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?.
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