A small block slides without friction down an inclined plane starting from rest. Let ${S_n}$be the distance travelled from time $t = n - 1$ to $t = n.$ Then $\frac{{{S_n}}}{{{S_{n + 1}}}}$ is
A small block slides without friction down an inclined plane starting from rest. Let ${S_n}$be the distance travelled from time $t = n - 1$ to $t = n.$ Then $\frac{{{S_n}}}{{{S_{n + 1}}}}$ is
- [IIT 2004]
- A
$\frac{{2n - 1}}{{2n}}$
- B
$\frac{{2n + 1}}{{2n - 1}}$
- C
$\frac{{2n - 1}}{{2n + 1}}$
- D
$\frac{{2n}}{{2n + 1}}$
Similar Questions
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- [AIPMT 2000]
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$Reason$ : Retardation is equal to the time rate of decrease of speed.
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- [AIIMS 2002]
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A monkey climbs up a slippery pole for $3$ and subsequently slips for $3$. Its velocity at time $t$ is given by $v (t) = 2t \,(3s -t)$ ; $0 < t < 3$ and $v(t) =\,-\, (t -3)\,(6 -t)$ ; $3 < t < 6$ $s$ in $m/s$. It repeats this cycle till it reaches the height of $20\, m$.
$(a)$ At what time is its velocity maximum ?
$(b)$ At what time is its average velocity maximum ?
$(c)$ At what time is its acceleration maximum in magnitude ?
$(d)$ How many cycles (counting fractions) are required to reach the top ?
A monkey climbs up a slippery pole for $3$ and subsequently slips for $3$. Its velocity at time $t$ is given by $v (t) = 2t \,(3s -t)$ ; $0 < t < 3$ and $v(t) =\,-\, (t -3)\,(6 -t)$ ; $3 < t < 6$ $s$ in $m/s$. It repeats this cycle till it reaches the height of $20\, m$.
$(a)$ At what time is its velocity maximum ?
$(b)$ At what time is its average velocity maximum ?
$(c)$ At what time is its acceleration maximum in magnitude ?
$(d)$ How many cycles (counting fractions) are required to reach the top ?