Q. A particle moves for $50$ seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be $5$ times the acceleration then the time for retardation is:
Motion in a Straight Line
Solution:
Let particle accelerates with acceleration $\alpha$ for time
$t_{1},$ and retard with retardation $-\beta $ for $ t_{2}$ $t_{1}+t_{2}=50$
CASE -1
CASE -2
$v = u + \alpha t_1$
$v = u -\beta t_2 $
$v = 0 + \alpha t_1$
$0 = u -\beta t_2 $
$v = \alpha t_1 $
$u=\beta t_2 $
Initial velocity is equal to the final velocity of $Case I. $
$\alpha t_{1}=\beta t_{2}$
$\alpha t_{1}=5 \alpha t_{2}$
$\alpha t_{1}=5 \alpha t_{2} \Rightarrow 5 t_{2}+t_{2}=50$
$6 t _{2}=50 \Rightarrow t _{2}=25 / 3 sec$
| CASE -1 | CASE -2 | |
|---|---|---|
| $v = u + \alpha t_1$ | $v = u -\beta t_2 $ | |
| $v = 0 + \alpha t_1$ | $0 = u -\beta t_2 $ | |
| $v = \alpha t_1 $ | $u=\beta t_2 $ | |