Question

A particle moves a distance x in the time t according to equation x=[t+5]^1/2 the acceleration of the particle is proportional to
A)distance^-2
B)velocity^3/2
C)acceleratin
D)Other

Answer 1

Answer:

$\boxed{\mathfrak{Acceleration \propto Distance^{-3} \ \ or \ \ Velocity^3}}$

Explanation:

Distance travelled:

$\rm x = {(t + 5)}^{ \frac{1}{2} } \\ \\ \rm x = \sqrt{(t + 5)}$

Velocity:

$\rm v = \dfrac{dx}{dt} \\ \\ \rm v = \frac{d}{dt} ( {(t + 5)}^{ \frac{1}{2} } ) \\ \\ \rm v = \dfrac{1}{2} (t + 5) ^{ - \frac{1}{2} } \\ \\ \rm v = \dfrac{1}{2 \sqrt{(t + 5)} }$

Accelration:

$\rm a = \dfrac{dv}{dt} \\ \\ \rm a = \dfrac{d}{dt} ( \dfrac{1}{2} (t + 5) ^{ - \frac{1}{2} } ) \\ \\ \rm a = - \dfrac{1}{4} (t + 5) ^{ - \frac{3}{2} } \\ \\ \rm a = - \frac{1}{4( \sqrt{ {(t + 5)} } ) ^{3} }$

So,

$\rm a \propto \dfrac{1}{ {x}^{3} } \\ \\ \rm a \propto {x}^{ - 3}$

or

$\rm a \propto {v}^{3}$

Answer 2

A particle moves a distance x in the time t according to equation x=[t+5]^1/2 the acceleration of the particle is proportional to

A)distance^-2

B)velocity^3/2

C)acceleratin

D)Other