Question

Starting from rest, Deepak paddles his bicycle to attain a velocity of $6m{s}^{-1}$ in $30seconds$. Then he applies brakes so that the velocity of the bicycle comes down to $4m{s}^{-1}$ in the next $5seconds$. Calculate the acceleration of the bicycle in both the cases.

• A. Case I : $a=0.2m{s}^{-2}$
  Case II: $a=0.4m{s}^{-2}$
• B. Case I : $a=0.2m{s}^{-2}$
  Case II: $a=-0.4m{s}^{-2}$
• C. Case I : $a=-0.2m{s}^{-2}$
  Case II: $a=-0.4m{s}^{-2}$
• D. Case I : $a=-0.2m{s}^{-2}$
  Case II: $a=0.4m{s}^{-2}$

Answer 1

The correct option is B Case I : $a=0.2m{s}^{-2}$

Case II: $a=-0.4m{s}^{-2}$

Case I :
$Initialvelocity,u=0,$
$Finalvelocity,v=6m{s}^{-1},$
$Time,t=30s$

Using the equation
$v=u+at$,
$6=0+30t$
$\Rightarrow a=0.2m{s}^{-2}$

Case II :
$Initialvelocity,u=6m{s}^{-1}$,
$Finalvelocity,v=4m{s}^{-1}$,
$Time,t=5s$
Using the equation
$v=u+at$,
$4=6+5a$
$\Rightarrow a=­–0.4m{s}^{-2}$