Question

According to this equation:
$△x=\frac{1}{2}a{t}^2$
We can determine how far an object, starting from rest, has traveled in the x direction if we know its constant acceleration and how long it has traveled.
Object M and object N both start from rest and have constant accelerations.
If object M has travelled for twice as much time as object N and object M's acceleration is three times that of object N, then how many times further has object M traveled than object N?

• A. $6$
• B. $12$
• C. $18$
• D. $36$
• E. Same distance

Answer 1

Answer: (B)

$12$

Distance traveled by object is given as $\Delta x=\frac{1}{2}a{t}^2$

$⟹$ $\frac{\Delta x_M}{\Delta x_N}=\frac{a_M{t}_M^2}{a_N{t}_N^2}$

Given : $t_M=2t_N$ $a_M=3a_N$

$\therefore$ $\frac{\Delta x_M}{\Delta x_N}=\frac{\left(3a_N\right)(2t_N{)}^2}{a_N{t}_N^2}=12$ $⟹\Delta x_M=12$ $\Delta x_N$