A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a = (4\hat i + 3\hat j)\ m/s^2$ and $\vec p = (8\hat i - 6\hat j)\ kg-m/s$ . The motion of the particle is
A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a = (4\hat i + 3\hat j)\ m/s^2$ and $\vec p = (8\hat i - 6\hat j)\ kg-m/s$ . The motion of the particle is
- A
uniform circular motion
- B
accelerated circular motion
- C
de-accelerated circular motion
- D
we can not say anything with $\vec a$ and $\vec p$ only
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A river is flowing due east with a speed $3\, ms^{-1}$. A swimmer can swim in still water at a speed of $4\, ms^{-1}$ (figure).
$(a)$ If swimmer starts swimming due north, what will be his resultant velocity (magnitude and direction) ?
$(b)$ If he wants to start from point A on south bank and reach opposite point $B$ on north bank,
$(i)$ Which direction should he swim ?
$(ii)$ What will be his resultant speed ?
$(c)$ From two different cases as mentioned in $(a)$ and $(b)$ above, in which case will he reach opposite bank in shorter time ?
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$(a)$ If swimmer starts swimming due north, what will be his resultant velocity (magnitude and direction) ?
$(b)$ If he wants to start from point A on south bank and reach opposite point $B$ on north bank,
$(i)$ Which direction should he swim ?
$(ii)$ What will be his resultant speed ?
$(c)$ From two different cases as mentioned in $(a)$ and $(b)$ above, in which case will he reach opposite bank in shorter time ?
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$\overrightarrow v \, = \,\overrightarrow {{v_0}} \, + \overrightarrow a t$ and $\overrightarrow r \, = \,\overrightarrow {{r_0}} \, + \overrightarrow {{v_0}} t\, + \,\frac{1}{2}g{t^2}$.
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$\overrightarrow v \, = \,\overrightarrow {{v_0}} \, + \overrightarrow a t$ and $\overrightarrow r \, = \,\overrightarrow {{r_0}} \, + \overrightarrow {{v_0}} t\, + \,\frac{1}{2}g{t^2}$.