The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:

1. \(5\hat{i}~\text{m/s}^2\) 2. \(-4\hat{i}~\text{m/s}^2\)
3. \(-8\hat{j}~\text{m/s}^2\) 4. \(0\)
Subtopic:  Acceleration |
 81%
From NCERT
NEET - 2017
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NEET 2023 - Target Batch - Aryan Raj Singh
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NEET 2023 - Target Batch - Aryan Raj Singh

A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant.  Based on the information given, which of the following is true?

1. Velocity and acceleration, both are parallel to r.
2. Velocity is perpendicular to r and acceleration is directed towards the origin.
3. Velocity is not perpendicular to r and acceleration is directed away from the origin.
4. Velocity and acceleration, both are perpendicular to r.
Subtopic:  Acceleration |
 70%
From NCERT
NEET - 2016
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
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To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh