First slide

Graphs

Question

Acceleration of a particle decreases exponentially from $10 m / s^{2}$ to $6 m / s^{2}$ . Write a - t equation.

Moderate

A

$a = 6 + 2 e^{- k t}$
B

$a = 3 + 4 e^{- k t}$
C

$a = 6 + 4 e^{- k t}$
D

None of these

Solution

a-t graph is as shown in figure.
Above $6 m / s^{2}$ the value $4 m / s^{2}$ decreases exponentially. Hence, a - t equation is
$a = 6 + 4 e^{- k t}$
Here, k is a positive constant
At t = 0,
$a = 6 + 4 e^{0} = 10 m / s^{2} as e^{0} = 1 At t = \infty a = 6 + 4 e^{- \infty} = 6 m / s^{2} as e^{- \infty} = 0$

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