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Standard IX

Physics

Acceleration

A particle mo...

Question

A particle moves for $8 s$ . It first accelerates from rest and then retards to rest. If the retardation be $3$ times the acceleration, then the time for which it accelerates will be

2 s

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3 s

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4 s

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6 s

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Solution

The correct option is C $6 s$
Let $t$ be the time of acceleration
Then retardation time $= 8 - t$
total time $= 8 s$
Let $V_{1}$ be velocity after acceleration
let acceleration be $a$
$\begin{matrix} V_{1} = u + a t h e r e u = 0 V_{1} = a t \to (i) \end{matrix}$
none retardation $= 3 a$ (given)
Hence,
$\begin{matrix} V = V_{1} - 3 a (8 - t) V = 0, & a s b o d y c o m e s t o r e s t V_{1} = 3 a (8 - t) a t = 3 a (8 - t), p u t V_{1} f r o m (i) t = 24 - 3 t 4 t = 24 t = 6 s e c o n d \end{matrix}$

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A particle moves for 8 s. It first accelerates from rest and then retards to rest. If the retardation be 3 times the acceleration, then the time for which it accelerates will be

A particle moves for $8 s$ . It first accelerates from rest and then retards to rest. If the retardation be $3$ times the acceleration, then the time for which it accelerates will be