A particle moves such that its position vector $\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{\mathrm{v}}(\mathrm{t})$ and acceleration $\overrightarrow{\mathrm{a}}(\mathrm{t})$ of the particle
A particle moves such that its position vector $\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{\mathrm{v}}(\mathrm{t})$ and acceleration $\overrightarrow{\mathrm{a}}(\mathrm{t})$ of the particle
- [JEE MAIN 2020]
- A
$\overrightarrow{\mathrm{v}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{a}}$ is directed towards the origin
- B
$\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\mathrm{a}}$ both are parallel to $\overrightarrow{\mathrm{r}}$
- C
$\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\mathrm{a}}$ both are perpendicular to $\overrightarrow{\mathrm{r}}$
- D
$\overrightarrow{\mathrm{v}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{a}}$ is directed away from the origin
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- [JEE MAIN 2024]
$Assertion$ : If a body is thrown upwards, the distance covered by it in the last second of upward motion is about $5\, m$ irrespective of its initial speed
$Reason$ : The distance covered in the last second of upward motion is equal to that covered in the first second of downward motion when the particle is dropped.
$Assertion$ : If a body is thrown upwards, the distance covered by it in the last second of upward motion is about $5\, m$ irrespective of its initial speed
$Reason$ : The distance covered in the last second of upward motion is equal to that covered in the first second of downward motion when the particle is dropped.
- [AIIMS 2000]
$Assertion$ : A tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth
$Assertion$ : A tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth
- [AIIMS 2009]