First slide

Instantaneous acceleration

Question

A particle moves a distance x in time t according to equation $x = {(t + 5)}^{- 1} .$ the acceleration of particle is proportional to:

Moderate

A

${(v e l o c i t y)}^{2 / 3}$
B

${(v e l o c i t y)}^{3 / 2}$
C

${(d i s \tan c e)}^{2}$
D

${(d i s \tan c e)}^{- 2}$

Solution

$x = \frac{1}{t + 5} v = \frac{- 1}{{(t + 5)}^{2}}; \frac{1}{(t + 5)} = v^{\frac{1}{2}} a = \frac{2}{{(t + 5)}^{3}} a = 2 v^{\frac{3}{2}}$

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