A particle moves with acceleration `a(t)` m/s^2 along an s-axis and has velocity `v_0` m/s at time `t=0` .  Find the displacement AND the distance traveled by the particle during the given time...

A particle moves with acceleration `a(t)` m/s^2 along an s-axis and has velocity `v_0` m/s at time `t=0` .  Find the displacement AND the distance traveled by the particle during the given time interval.

`a(t)=9` ; `v_0=-1` ; `0lt=tlt=2`

1 Answer

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The distance D traveled by a particle in a duration of time t is D = u*t + (1/2)*a*t^2 where u is the the initial velocity and a is the acceleration.

If the acceleration of the particle is 9 m/s^2 and the initial velocity is -1 m/s:

distance traveled in 0 seconds is 0

distance traveled in 2 seconds is -1*2 + 0.5*9*4 = 16

The distance traveled by the particle in the given time interval is 16 m, this is the same as its displacement.