Question 159: Motion in 1D

Question

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t $$-$$ t
3
.  How long would the particle travel before coming to rest ?

Accepted Answer

Given x = 40 + 12t $$-$$ t
3
v = $${{dx} \over {dt}}$$ = 12 - 3t
2
When particle comes to rest then v = 0.
$$ 	herefore $$ 12 - 3t
2
= 0
$$ \Rightarrow $$ t = 2 s
Distance travelled before coming to rest,
s = $$\int\limits_0^2 {vdt} $$ = $$\int\limits_0^2 {\left( {12 - 3{t^2}} ight)dt} $$
= $${\left[ {12t - {{3{t^3}} \over 3}} ight]_0^2}$$
= 24 - 8 = 16 m

Answer

16 m

Answer

24 m

Answer

40 m

Answer

56 m

Motion in 1D

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t $-$ t 3 . How long would the particle travel before coming to rest ?

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