A particle moves along a straight line OX. At a time t (in seconds) the distance x (in meters) of the particle from O is given by x = 40 + 12t – t 3 How long would the particle travel before coming to rest?
Text Solution
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Velocity is rate of change of distance or displacement
Distance travelled by the particle is
x = 40 + 12t – t 3
we know that, velocity is rate of change of displacement, e.,m v = 
.
∴ v = 
(40 + 12t – t3) = 0 + 12 – 3t 2
but final velocity v = 0
∴ 12 – 3t 2 = 0
or ; t 2 = 
= 4
or ; t = 2 s
Hence, position of the particle at t = 2 sec.
x = 40 + 12 – 3
= 40 + 24 – 8 = 64 – 8
= 56 m
position of particle at t = 0 sec.
t = 0
x = 40 m
distance travelled by particle in 2 sec. = 56 – 40 = 16m
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