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Syakirin: a) A body moves along the x-axis with displacement x cm where x(t)=10[t−ln(t+1)], t≥0 and t is the time in seconds. Find the object's velocity and acceleration after being in motion for 1 second. b) A particle moves in such a way that its displacement, x cm, t seconds after starting to move from a fixed point O is given by x(t)=10+20e^-0.2t, t≥0 i) Determine the rate if change of its displacement at time t=5. ii) Will this particle ever maintain a constant velocity for a period of time? iii) Will this particle ever maintain a constant acceleration for a period of time?
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  • August 29, 2014 at 12:54am
  • ShamSuiisses:(a) velocity = displacement / time t = 1 velocity = (10 [(1) - ln((1)+1)] / 1) cm/s velocity = (10 [1 - ln(2)] / 1) cm/s (put this into the calculator and calculate) acceleration = velocity / time acceleration = (velocity / 1) cm/s^2
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    • August 29, 2014 at 4:58am
  • ShamSuiisses:(b) (i) rate of change = velocity velocity = displacement / time t = 1 velocity = (10+20e^-0.2(5)) cm/s (put this into the calculator and calculate)
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    • August 29, 2014 at 5:04am
  • ShamSuiisses:(ii) calculate velocity using equation : x(t)=10+20e^-0.2t, t≥0 where time is t = 6. Compare the value with part (i). If the answer is same, velocity is constant. If not, its otherwise. It would be the same for part (iii) also if im not wrong, but just do the calculations aswell.
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    • August 29, 2014 at 5:06am
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