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X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is?
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X and Y coordinates of a particle at any time T are given by X is equa...
Acceleration of particle is 18m/s^2 at the and of 5 second.
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X and Y coordinates of a particle at any time T are given by X is equa...
Coordinates of the Particle
The x-coordinate of the particle at any time t is given by the equation: X = 7t - 4t^2.
The y-coordinate of the particle at any time t is given by the equation: Y = 5t.
Calculating the Acceleration
Acceleration is the rate at which the velocity of an object changes with time. It is the second derivative of the position function with respect to time.
To find the acceleration of the particle at t = 5 seconds, we need to calculate the second derivative of the position function with respect to time.
Step 1: Calculating the First Derivative of X
To find the velocity function, we need to calculate the first derivative of the position function X with respect to time (t).
Differentiating X = 7t - 4t^2 with respect to t:
dX/dt = 7 - 8t
The velocity function is given by dX/dt.
Step 2: Calculating the First Derivative of Y
To find the velocity function, we need to calculate the first derivative of the position function Y with respect to time (t).
Differentiating Y = 5t with respect to t:
dY/dt = 5
The velocity function is given by dY/dt.
Step 3: Calculating the Second Derivative of X
To find the acceleration function, we need to calculate the second derivative of the position function X with respect to time (t).
Differentiating dX/dt = 7 - 8t with respect to t:
d^2X/dt^2 = -8
The acceleration function is given by d^2X/dt^2.
Step 4: Calculating the Second Derivative of Y
To find the acceleration function, we need to calculate the second derivative of the position function Y with respect to time (t).
Differentiating dY/dt = 5 with respect to t:
d^2Y/dt^2 = 0
The acceleration function is given by d^2Y/dt^2.
Step 5: Finding the Acceleration at t = 5 seconds
Now that we have the acceleration functions for both the x and y coordinates, we can calculate the acceleration at t = 5 seconds.
Substituting t = 5 in the acceleration functions:
Acceleration in the x-direction: d^2X/dt^2 = -8
Acceleration in the y-direction: d^2Y/dt^2 = 0
Therefore, the acceleration of the particle at t = 5 seconds is -8 m/s^2 in the x-direction and 0 m/s^2 in the y-direction.
The x-coordinate of the particle at any time t is given by the equation: X = 7t - 4t^2.
The y-coordinate of the particle at any time t is given by the equation: Y = 5t.
Calculating the Acceleration
Acceleration is the rate at which the velocity of an object changes with time. It is the second derivative of the position function with respect to time.
To find the acceleration of the particle at t = 5 seconds, we need to calculate the second derivative of the position function with respect to time.
Step 1: Calculating the First Derivative of X
To find the velocity function, we need to calculate the first derivative of the position function X with respect to time (t).
Differentiating X = 7t - 4t^2 with respect to t:
dX/dt = 7 - 8t
The velocity function is given by dX/dt.
Step 2: Calculating the First Derivative of Y
To find the velocity function, we need to calculate the first derivative of the position function Y with respect to time (t).
Differentiating Y = 5t with respect to t:
dY/dt = 5
The velocity function is given by dY/dt.
Step 3: Calculating the Second Derivative of X
To find the acceleration function, we need to calculate the second derivative of the position function X with respect to time (t).
Differentiating dX/dt = 7 - 8t with respect to t:
d^2X/dt^2 = -8
The acceleration function is given by d^2X/dt^2.
Step 4: Calculating the Second Derivative of Y
To find the acceleration function, we need to calculate the second derivative of the position function Y with respect to time (t).
Differentiating dY/dt = 5 with respect to t:
d^2Y/dt^2 = 0
The acceleration function is given by d^2Y/dt^2.
Step 5: Finding the Acceleration at t = 5 seconds
Now that we have the acceleration functions for both the x and y coordinates, we can calculate the acceleration at t = 5 seconds.
Substituting t = 5 in the acceleration functions:
Acceleration in the x-direction: d^2X/dt^2 = -8
Acceleration in the y-direction: d^2Y/dt^2 = 0
Therefore, the acceleration of the particle at t = 5 seconds is -8 m/s^2 in the x-direction and 0 m/s^2 in the y-direction.
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X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is?
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X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is?.
X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X and Y coordinates of a particle at any time T are given by X is equals to 7t+ 4t^2 and Y is equals to 5t where x and y are in metre and t is in seconds the acceleration of a particle at t = 5 second is?.
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