Question 157: Motion in 1D

Question

The positions x of a particle with respect to time t along x-axis is given by x = 9t
2
$$-$$ t
3
where x is in metres and  t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

Accepted Answer

Speed v = $${{dx} \over {dt}}$$ = $${d \over {dt}}\left( {9{t^2} - {t^3}} ight)$$ = 18t - 3t
2
At maximum speed
$${{dv} \over {dt}}$$ = 0
$$ \Rightarrow $$ 18 - 6t = 0
$$ \Rightarrow $$ t = 3
$$ 	herefore $$ Position of the particle  = 81 - 27 = 54 m

Answer

54 m

Answer

81 m

Answer

24 m

Answer

32 m

Motion in 1D

The positions x of a particle with respect to time t along x-axis is given by x = 9t 2 $-$ t 3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

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