Ncert Exercises & Solutions

Give an example of a motion where x > 0, v < 0, a > 0 at a particular instant.

Hint: $Velocity, v = \frac{dx}{dt} and acceleration, a = \frac{dv}{dt} .$ $Velocity, v = \frac{dx}{dt} and acceleration, a = \frac{dv}{dt} .$

Step 1: Let the motion is represented by

$x (t) = A + {Be}^{- γt} . . . (i)$ $x (t) = A + {Be}^{- γt} . . . (i)$
$Where A > B and γ > 0$ $Where A > B and γ > 0$
$Step 2 : Calculate velocity$ $Step 2 : Calculate velocity$
$Now velocity, v (t) = \frac{dx}{dt} = - {Bγe}^{- γt}$ $Now velocity, v (t) = \frac{dx}{dt} = - {Bγe}^{- γt}$
$Step 3 : Calcuate acceleration$ $Step 3 : Calcuate acceleration$
$Acceleration, a (t) = \frac{dv}{dt} = {Bγ}^{2} e^{- γt}$ $Acceleration, a (t) = \frac{dv}{dt} = {Bγ}^{2} e^{- γt}$

Step 4: At any time t

Suppose we are considering any instant t, then from Eq. (i), we can say that
x(t) > 0 v(t) < 0 and a > 0.

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