First slide

Rectilinear Motion

Question

The relation between time t and distance x is $t = α x^{2} + β x$ where $α$ and $β$ are constants. The retardation is

Difficult

A

$2 α v^{3}$
B

$2 β v^{3}$
C

$2 α β v^{3}$
D

$2 β^{2} v^{3}$

Solution

$\begin{array}{l} t = α x^{2} + β x \\ Differentiating: 1 = 2 α \frac{d x}{d t} \cdot x + β \frac{d x}{d t} \\ v = \frac{d x}{d t} = \frac{1}{β + 2 α x}; \frac{d v}{d t} = \frac{- 2 α v}{(β + 2 α x)^{2}} = - 2 α v^{3} \end{array}$

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