Question

A particle performs rectilinear motion in such a way that its initial velocity has opposite direction with its uniform acceleration. Let $x_A$ and $x_B$ be the magnitude of displacements in the first 10 seconds and the next 10 seconds then :

• A. $x_A<x_B$
• B. $x_A=x_B$
• C. $x_A>x_B$
• D. The information is not sufficient to decide the ralation of $x_A$ with $x_B$.

Answer 1

The correct option is D The information is not sufficient to decide the ralation of $x_A$ with $x_B$.

$s=ut+\left(1/2\right)a{t}^2$

Let u be magnitude of initial velocity and a be magnitude of initial acceleration

After 10 s, displacement $s_{10}=10u-50a$

After 20s, displacement $s_{20}=20u-200a$

$x_a=|s_{10}-s_0|=|10u-50a|$

$x_b=|s_{20}-s_{10}|=|10u-150a|$

Consider two cases, $\left(i\right)u=5a,\left(ii\right)u=15a$

For case (i), $x_b>x_a$

For case (ii), $x_a>x_b$

Since the results are contradictory, no conclusion can be drawn for the relationship between $x_a\&x_b$ unless magnitude of u and a is given.