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

The Equation for the Path of Projectile

The initial v...

Question

The initial velocity of a particle moving along $x -$ axis is $u (a t t = 0 a n d x = 0)$ and its acceleration a is given by $a = k x$ . Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?

v^{2} - u^{2} = 2 k x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

v^{2} = u^{2} + 2 k x^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

v^{2} = u^{2} + k x^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

v^{2} + u^{2} = 2 k x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $v^{2} = u^{2} + k x^{2}$
a = kx
$a = \frac{d v}{d t} = \frac{d v}{d x} \times \frac{d x}{d t}$
Vdv = adx
= kx dx
$\frac{V^{2}}{2} = \frac{k x^{2}}{2} + C$
at $t = 0 c = 0 v e l o c i t y = u$
So
$C = \frac{U^{2}}{2} V^{2} = u^{2} + k x^{2}$
Hence option (C) is correct

Suggest Corrections

Similar questions

Q. A point moving with constant acceleration from

A

B

in the straight line

A B

has velocities

u

and

v

A

and

B

respectively. Find its velocity at

C

, the mid point of

A B

A body is moving with an initial velocity of $u$ and having constant acceleration $a$ . The final velocity $v$ can be obtained by using which of the following equation of motion if a body covers a distance $s$ .

Q. A particle executing SHM has velocities

u

and

v

and accelerations

a

and

b

at two of its positions. Find the shortest distance between these two positions.

Q. Derive an equation for position-velocity relation

(2 a s = v^{2} - u^{2})

by graphical method

Q. Check the accuracy of relation

v^{2} - u^{2} = 2 a s

, where

v

and

u

are final and initial velocities,

a

is the acceleration, and s is the distance.

Join BYJU'S Learning Program

The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx. Which of the following equation is correct between its velocity (v) and position (x)?

The correct option is C v2=u2+kx2a = kx a=dvdt=dvdx×dxdtVdv = adx = kx dxV22=kx22+Cat t=0c=0velocity=uSo C=U22V2=u2+kx2 Hence option (C) is correct

The initial velocity of a particle moving along $x -$ axis is $u (a t t = 0 a n d x = 0)$ and its acceleration a is given by $a = k x$ . Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?

The correct option is C $v^{2} = u^{2} + k x^{2}$
a = kx
$a = \frac{d v}{d t} = \frac{d v}{d x} \times \frac{d x}{d t}$
Vdv = adx
= kx dx
$\frac{V^{2}}{2} = \frac{k x^{2}}{2} + C$
at $t = 0 c = 0 v e l o c i t y = u$
So
$C = \frac{U^{2}}{2} V^{2} = u^{2} + k x^{2}$
Hence option (C) is correct