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  • 5 years ago

A particle moves on a straight line so that its velocity at time t is given by v = sqrt(s) where s is the distance from the origin. s=1 when t=0, then what is the value of s when t=1 ? I tried using parameters but I couldn't find a good way ... can someone help ?

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  1. Yuki
    • 5 years ago
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    I would really love to have some help ... :(

  2. dumbcow
    • 5 years ago
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    velocity is rate of distance/time v=ds/dt = sqrt(s) rearrange variables so s is with ds ds/sqrt(s) = dt now integrate both sides integral 1/sqrt(s) = integral s^-1/2 = 2*s^1/2 = 2sqrt(s) 2sqrt(s) = t + C solve for s sqrt(s) = t/2 + C s = (t/2 +C)^2 = t^2/4 +Ct +C^2 find C using initial conditions s=1 when t=0 1=C^2 -->C=1 s = t^2/4 + t + 1 when t=1 s = 1/4+1+1 = 2.25 Hope this helps

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