JEE Main 20208 JanuaryEvening Shift
- Exam
- JEE Main
- Year
- 2020
- Date
- 8 January
- Shift
- Evening Shift
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
JEE Main 2020 · 8 January · Evening Shift · Physics · Motion in Two Dimensions
A particle moves such that its position vector → r (t) = cos ^ i +...
A particle moves such that its position vector \overset{\to}{r}\left(t\right) = cos \omegat\overset{^}{i} + sin \omegat\overset{^}{j} where is a constant and is time. Then which of the following statements is true for the velocity \overset{\to}{a}\left(t\right) of the particle:
Options
- A is perpendicular to and is directed away from the origin
- B and both are perpendicular to
- C and both are parallel to
- D is perpendicular to and is directed towards the origin
Correct answer
D. is perpendicular to and is directed towards the origin
Step-by-step solution
\overset{\to}{r} = cos \omegat\overset{^}{i} + sin \omegat\overset{^}{j}
\overset{\to}{v} = \dfrac{d\overset{\to}{r}}{dt} = \omega\left(- sin \omegat\overset{^}{i} + cos \omegat\overset{^}{j}\right)
\overset{\to}{a} = \dfrac{d\overset{\to}{v}}{dt} = - {\omega}^{2}\left(cos \omegat\overset{^}{i} + sin \omegat\overset{^}{j}\right)
is antiparallel to
So
\overset{\to}{v} = \dfrac{d\overset{\to}{r}}{dt} = \omega\left(- sin \omegat\overset{^}{i} + cos \omegat\overset{^}{j}\right)
\overset{\to}{a} = \dfrac{d\overset{\to}{v}}{dt} = - {\omega}^{2}\left(cos \omegat\overset{^}{i} + sin \omegat\overset{^}{j}\right)
is antiparallel to
So