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The motion of a body is given by the equation {dv}{dt} = 6-3v:

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The motion of a body is given by the equation $\frac{d v}{d t} = 6 - 3 v :$ where $v$ is in $m / s$ . If the body was at rest at $t = 0$
(i) the terminal speed is $2 m / s$
(ii) the magnitude of the initial acceleration is $6 m / s$
(iii) the speed varies with time as $v = 2 (1 - e^{- 3 t}) m / s$
(iv) The speed is $1 m / s$ , when the acceleration is half the initial

(i), (iii)

(ii), (iii), (i v)

(i), (ii), (iii)

A ll

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Charlotte Discussed

The motion of a body is given by the equation

\frac{d v}{d t} = 6 - 3 v :

where

v

is in

m / s

. If the body was at rest at

t = 0

(i) the terminal speed is

2 m / s

(ii) the magnitude of the initial acceleration is

6 m / s

(iii) the speed varies with time as

v = 2 (1 - e^{- 3 t}) m / s

(iv) The speed is

1 m / s

, when the acceleration is half the initial

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Text solutionVerified

$\frac{d v}{d t} = 6 - 3 v$

$\int \frac{d v}{6 - 3 v} = \int d t$

$- \frac{1}{3} lo g ∣ 2 - v ∣ = d t$

$- lo g ∣ 2 - v ∣ = 3 t$

$∣ 2 - v ∣ = e^{- 3 t}$

$2 - e^{- 3 t} = v$

Initial acceleration is $0$ .

At $t = 0$ , terminal velocity is $v = 2 m / s$

Hence, condition 1 and 3 are correct.

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Question Text	The motion of a body is given by the equation $\frac{d v}{d t} = 6 - 3 v :$ where $v$ is in $m / s$ . If the body was at rest at $t = 0$ (i) the terminal speed is $2 m / s$ (ii) the magnitude of the initial acceleration is $6 m / s$ (iii) the speed varies with time as $v = 2 (1 - e^{- 3 t}) m / s$ (iv) The speed is $1 m / s$ , when the acceleration is half the initial
Answer Type	Text solution:1
Upvotes	150