A particle moves with a non zero initial velocity $v_{0}$ and retardation $k v$ , where $v$ is the velocity at any time $t$ .

Question

Verified by Toppr

Answer 1

$u = v_{0},$ retardation $a = k v$ and $v$ is the velocity at time $t$ .
using $v = u - a t,$ we will get $v = v_{0} - k v t \Rightarrow t = \frac{v _{0}}{k v} - \frac{1}{k}$
if $v = 0, t = \infty$ . So the particle will be moved for a long time.

Answer 2

u = v_{0},

retardation

a = k v

and

v

is the velocity at time

t

.
using

v = u - a t,

we will get

v = v_{0} - k v t \Rightarrow t = \frac{v _{0}}{k v} - \frac{1}{k}

if

v = 0, t = \infty

. So the particle will be moved for a long time.

A particle moves with a non zero initial velocity $v_{0}$ and retardation $k v$ , where $v$ is the velocity at any time $t$ .

The particle will cover a total distance $\frac{v _{0}}{k}$

The particle comes to rest at $t = \frac{1}{k}$

Particle continues to move for long time

at time $\frac{1}{α}, v = \frac{v _{0}}{2}$

$u = v_{0},$ retardation $a = k v$ and $v$ is the velocity at time $t$ .
using $v = u - a t,$ we will get $v = v_{0} - k v t \Rightarrow t = \frac{v _{0}}{k v} - \frac{1}{k}$
if $v = 0, t = \infty$ . So the particle will be moved for a long time.

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plots shown in figure, indicate the one that represents the velocity ( $v$ ) of the pebble as a function of time ( $t$ ).

A particle having initial velocity u moves with a constant acceleration a for a time $t .$ Evaluate it for $u = 5 m / s, a = 2 m / s$ and $t = 10 s .$

A particle moves along the x-direction with constant acceleration. The displacement, measured form a convenient position, is 2 m at time t = 0 and is zero when t = 10 s. If the velocity of the particle is momentary zero when t = 6s, determine the acceleration a the velocity v when t = 10s.

A particle moving with a non-zero velocity and constant acceleration on straight line travels $15 m$ in first $3 s$ and $33 m$ in next $3 s$ in the same direction, find
(i) initial velocity of particle
(ii) acceleration of particle

Revise with Concepts

Velocity - Time Relation in Uniform Accelerated Motion

Position - Time Relation in Uniform Accelerated Motion

Position - Velocity Relation in Uniform Accelerated Motion

Derivation of Equations of Motion in One Dimension Using Calculus

Displacement in Nth Second

A particle moves with a non zero initial velocity v0​ and retardation kv, where v is the velocity at any time t.

The particle will cover a total distance kv0​​

The particle comes to rest at t=k1​

Particle continues to move for long time

at time α1​,v=2v0​​

u=v0​, retardation a=kv and v is the velocity at time t. using v=u−at, we will get v=v0​−kvt⇒t=kvv0​​−k1​ if v=0,t=∞. So the particle will be moved for a long time.

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plots shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).

A particle having initial velocity u moves with a constant acceleration a for a time t. Evaluate it for u=5m/s,a=2m/s and t=10s.

A particle moves along the x-direction with constant acceleration. The displacement, measured form a convenient position, is 2 m at time t = 0 and is zero when t = 10 s. If the velocity of the particle is momentary zero when t = 6s, determine the acceleration a the velocity v when t = 10s.

A particle moving with a non-zero velocity and constant acceleration on straight line travels 15 m in first 3 s and 33 m in next 3 s in the same direction, find (i) initial velocity of particle (ii) acceleration of particle

Revise with Concepts

Velocity - Time Relation in Uniform Accelerated Motion

Position - Time Relation in Uniform Accelerated Motion

Position - Velocity Relation in Uniform Accelerated Motion

Derivation of Equations of Motion in One Dimension Using Calculus

Displacement in Nth Second

A particle moves with a non zero initial velocity $v_{0}$ and retardation $k v$ , where $v$ is the velocity at any time $t$ .

The particle will cover a total distance $\frac{v _{0}}{k}$

The particle comes to rest at $t = \frac{1}{k}$

at time $\frac{1}{α}, v = \frac{v _{0}}{2}$

$u = v_{0},$ retardation $a = k v$ and $v$ is the velocity at time $t$ .
using $v = u - a t,$ we will get $v = v_{0} - k v t \Rightarrow t = \frac{v _{0}}{k v} - \frac{1}{k}$
if $v = 0, t = \infty$ . So the particle will be moved for a long time.

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plots shown in figure, indicate the one that represents the velocity ( $v$ ) of the pebble as a function of time ( $t$ ).

A particle having initial velocity u moves with a constant acceleration a for a time $t .$ Evaluate it for $u = 5 m / s, a = 2 m / s$ and $t = 10 s .$

A particle moving with a non-zero velocity and constant acceleration on straight line travels $15 m$ in first $3 s$ and $33 m$ in next $3 s$ in the same direction, find
(i) initial velocity of particle
(ii) acceleration of particle