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Graphs

Question

Velocity of a particle increases exponentially with time from 2 m/s to 6 m/s. Write v-t equation corresponding to it.

Moderate

A

$v = 2 + 4 (1 - e^{k t})$
B

$v = - 2 + 4 (1 - e^{- k t})$
C

$v = 2 + 4 (1 - e^{- k t})$
D

$v = 2 - 4 (1 - e^{- k t})$

Solution

v-t graph is as shown in figure,
Above 2 m/s, the value 4 m/s increases exponentially. Hence, vt equation is
$v = 2 + 4 (1 - e^{- k t})$
Here k is a positive constant, which will depend on factors which are not given in the question.
At t = 0,
$v = 2 + 4 (1 - e^{0})$
v = 2 m/s
At t = $\infty$
$v = 2 + 4 (1 - e^{- \infty})$
v = 6 m/s

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