Displacement x , of a body moving in one-dimensional motion depen… - Vidyadip

MCQ

Displacement x , of a body moving in one-dimensional motion depends on time $t$ as follows : $x=a_0+a_1 t+a_2 t^2+a_3 t^3$ where $a_0, a_1, a_2, a_3$ are fixed.
Then the correct statement is :

A
The position of the particle is $a _1$.
B
The initial velocity of the particle is $2 a _2$.
✓
The acceleration of the particle is not constant.
D
Position time curve is a straight line.

✓

Answer

Correct option: C.

The acceleration of the particle is not constant.

(c) $
x=a_0+a_1 t+a_2 t^2+a_3 t^3
$
Position $t =0$
$
\begin{aligned}
& =a_0 \\
v & =\frac{d x}{d t}=a_1+2 a_2 t+3 a_3 t^2
\end{aligned}
$
Velocity $t =0$
$
v=a_1
$
Acceleration $a =\frac{ dv }{ dt }=2 a _2+6 a _3 t$
Here, acceleration depends on time, hence it is not constant. Hence the correct option is (c).

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