Question

The position of a particle along the x-axis at certain times is given below:

$t\left(s\right)$	$0$	$1$	$2$	$3$
$X\left(m\right)$	$-2$	$0$	$6$	$16$

Which of the following describes the motion correctly?

• A. Uniform acceleration
• B. Uniform retardation
• C. Non-uniform acceleration
• D. There is no enough data for generalization

Answer 1

The correct option is A Uniform acceleration

From the table, we will find out velocity at each interval;-

t	0	1	2	3
x(m)	-2	0	6	16
$v=\frac{△x}{△t}$	-	2	6	10

$\left[\begin{array}{c}△x=x\hat{i}-x\hat{i}-1\\ △t=t\hat{i}-t\hat{i}-1=1\end{array}\right]$

Clearly, $v$ now varies with $t$ linearly as $v=4t-2$

This. $\frac{dv}{dt}=4$, which is constant >0

$\Rightarrow$ It is a unifformly accelerated motion.