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  1. A particle moves along the curve

Ask by Stanley Nunez. in Nigeria
Jan 22,2025

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Answer

At time , the velocity component in the direction is and the acceleration component is .

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Beyond the Answer

To find the components of the velocity and acceleration of the particle at time , we first need to compute the velocity vector by differentiating the position functions , , and with respect to time .
The velocity components are given by:
At :
Thus, the velocity vector is .
Next, we compute the acceleration vector by differentiating the velocity components:
This gives us the acceleration vector as .
To find the components of both vectors in the direction of , we first need to normalize this direction vector:
The unit direction vector is then:
Now, to project the velocity and acceleration onto this direction, we use the dot product:
Thus, the final results for the components of the velocity and acceleration at in the specified direction are:

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