Question

The ratio of distances travelled by two bodies A and B starting from rest moving along a straight line with equal acceleration is n, then (Assume $t_A,t_B$ as time taken by bodies A and B respectively).

• A. $t_A\ge t_B$, if $n\ge 1$
• B. $t_A\le t_B$, if $n\le 2$
• C. $t_A=t_B$, if $n=1$
• D. $t_A>t_B$, if $n<1$

Answer 1

Answer: (A), (C)

The correct options are
A $t_A\ge t_B$, if $n\ge 1$
C $t_A=t_B$, if $n=1$

Given $u=0$

Let distance travelled by by Bodies A = $S_A$,

Let distance travelled by by Bodies B = $S_B$,

Let acceleration is $a$.

Using $s=ut+\frac{1}{2}a{t}^2$

$\frac{S_A}{S_B}=\frac{\frac{1}{2}a{t}_A^2}{\frac{1}{2}a{t}_b^2}$ $\Rightarrow \frac{S_A}{S_B}=\frac{t_A^2}{t_B^2}=n$,

If $n\ge 1$, $\frac{t_A^2}{t_B^2}\ge 1$ $\Rightarrow t_A\ge t_B$,

If n=1, $\frac{t_A^2}{t_B^2}=1$ $\Rightarrow t_A=t_B$