MyQuestionIcon

1

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

Acceleration

The accelerat...

Question

The acceleration of a particle is $a = a_{0} - b v$ , where $v$ is velocity at instant $t$ . If the particle starts from rest at $t$ =0, find the velocity of the particle as the function of time.

Open in App

Solution

$a = a_{0} - b v \frac{d v}{d t} = a_{0} - b v \int_{0}^{v} \frac{d v}{a_{0} - b v} \int_{0}^{t} d t \frac{- l n}{b} (a_{0} - b v) = t + l n C a_{0} - b v = e^{- b t} v = \frac{a_{0} - e^{- b t}}{b}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A particle is executing SHM with amplitude

A

T

, maximum acceleration

a_{0}

and maximum velocity

v_{0}

. It starts from mean position at

t = 0

t

it has the displacement

A / 2

a

v

Q. The acceleration

a

m s^{- 2}

of a particle is given by

a = 3 t^{2} + 2 t + 2

t

is the time. If the particle starts out with a velocity

v = 2 m s^{- 1}

t = 0

, then find the velocity at the end of

2 s

Q. The acceleration of a particle varies with time

t

seconds according to the relation

a = 6 t + 6 m s^{- 2}

. Find velocity and position as functions of time. It is given that the particle starts from origin at

t = 0

2 m s^{- 1}

Q. A particle starts from rest at

t = 0

and moves in a straight line with acceleration as shown in the following figure.

The velocity of the particle at

t = 3

Q. The acceleration of a particle as a function of time

t

a = k . t^{5 / 2}

. If initial speed of the particle

(a t t = 0)

u

then its velocity

v

as a function of time

t

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Acceleration

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon