Question

A particle starts from rest and moves with constant acceleration. Its distance x and velocity v is related as

• A. $x\propto v$
• B. $x\propto v^2$
• C. $x\propto v^3$
• D. $x\propto v^4$

Answer 1

The correct option is B

$x\propto v^2$

Step 1: Given data:

A particle starts from rest and moves with constant acceleration

Step 2: From the equations of motion we have:

$v^2-u^2=2as$

Here,

s = x is the distance

u = 0 is the initial velocity

v is the final velocity

a = constant acceleration

Step 3: Finding the relation between x and v:

$$\begin{gathered} v^2-u^2=2as \\ {v}^2=2a\times x \\ x=\frac{v^2}{2a} \\ Sinceaiscons\tan t, \\ x\propto v^2 \end{gathered}$$

Hence, the correct option is (B).