The position of a particle moving in the x-y plane at any time t is given by, x=(3 t^3-6 t) metres; y=(t^2-2 t) metres. Select the correct statement.

Correct answer: C. velocity is zero at t=1 ~s aligned & x=3 t²-6 t, So (velocity) )_x=(d x)/(d t)=6 t-6 ; & y=t²-2 t aligned So, ( velocity )_y=(d y)/(d t)=2 t-2 At time t=1 , = (d x)/(d t)= 6 × 1-6=0 and (d y)/(d t)= 2 × 1-2=0 .

AIIMS 2010

Exam: AIIMS
Year: 2010
Subject: Physics
Chapter: Motion in One Dimension

AIIMS 2010 · Physics · Motion in One Dimension

The position of a particle moving in the x-y plane at any time t is...

The position of a particle moving in the

x-y

plane at any time

t

is given by,

x=\left(3 t^3-6 t\right)

metres;

y=\left(t^2-2 t\right)

metres. Select the correct statement.

Options

Aacceleration is zero at $t=0$
Bvelocity is zero at $t=0$
Cvelocity is zero at $t=1 \mathrm{~s}$
Dvelocity and acceleration of the particle are never zero.

Correct answer

C. velocity is zero at $t=1 \mathrm{~s}$

Step-by-step solution

\begin{aligned}& x=3 t²-6 t, \text{ So (velocity) }\right)_x=\frac{d x}{d t}=6 t-6 \text{; }\\ & y=t²-2 t \end{aligned}

So,

(\text{ velocity })_y=\frac{d y}{d t}=2 t-2

At time

t=1

, =

\frac{d x}{d t}=

\times

1-6=0

\text{\text{ and } } \frac{d y}{d t}=

\times

1-2=0 .

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