You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Relative Velocity

Positions of ...

Question

Positions of two particles $A$ and $B$ as a function of time are given by $X_{A} = - 3 t^{2} + 8 t + c$ and $Y_{B} = 10 - 8 t^{3}$ . The velocity of $B$ with respect to $A$ at $t = 1$ is $\sqrt{v}$ . Find $v$ [in $m^{2} / s^{2}$ ]

Open in App

Solution

As we know,
$\frac{d x}{d t} = v$
$X_{A} = - 3 t^{2} + 8 t + c$
$\Rightarrow \frac{d {\to X}_{A}}{d t} = {\to v}_{A} = (- 6 t + 8)^i$
$\Rightarrow {\to v}_{A} (t = 1 s) = 2^i m/s$

$Y_{B} = 10 - 8 t^{3}$
$\Rightarrow \frac{d {\to Y}_{B}}{d t} = {\to v}_{B} = - 24 t^{2}^j$
$\Rightarrow {\to v}_{B} (t = 1 s) = - 24^j m/s$
Therefore,
$| {\to v}_{B, A} | = ∣ ∣ {\to v}_{B} - {\to v}_{A} ∣ ∣ = ∣ ∣ - 24^j - 2^i ∣ ∣$
$= \sqrt{24^{2} + 2^{2}} = \sqrt{580} m/s$
$\Rightarrow ∣ ∣ {\to v}_{B} - {\to v}_{A} ∣ ∣ = \sqrt{v} = \sqrt{580}$ [as given]
So, $v = 580 m^{2} / s^{2}$

Suggest Corrections

Similar questions

Q. A particle is moving along the

x -

axis, with its coordinate with time

^{'} t^{'}

given by

x (t) = 10 + 8 t - 3 t^{2}

. Another particle is moving along the

y -

axis, with its coordinate as a function of time given by

y (t) = 5 - 8 t^{3}

. At

t = 1 s

, the speed of the second particle as measured in the frame of the first particle is given as

\sqrt{v}

. Then

v

(in m/s)

Q. The velocity

v

of a particle at time

t

is given by

v = a t + \frac{b}{t + c}

, where

a, b

and

c

are constant. The dimensions of

a, b

and

c

are respectively.

The velocity $v$ of a particle at time $t$ is given by $v = a t + \frac{b}{t + c}$ where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are respectively :

Q. The velocity

v

of a particle at time

t

is given by

v = a t + \frac{b}{t + c}

, where

a, b

and

c

are constants. The dimensions of

a, b

and

c

are respectively

Q. The velocity

v

of a particle at time

t

is given by

v = a t + \frac{b}{t + c}

, where

a, b a n d c

are constants.The dimensions of

a, b a n d c

are respectively:

Join BYJU'S Learning Program

Explore more

Relative Velocity

Standard XII Physics

Join BYJU'S Learning Program

Positions of two particles A and B as a function of time are given by XA=−3t2+8t+c and YB=10−8t3. The velocity of B with respect to A at t=1 is √v. Find v [in m2/s2]

Positions of two particles $A$ and $B$ as a function of time are given by $X_{A} = - 3 t^{2} + 8 t + c$ and $Y_{B} = 10 - 8 t^{3}$ . The velocity of $B$ with respect to $A$ at $t = 1$ is $\sqrt{v}$ . Find $v$ [in $m^{2} / s^{2}$ ]