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Find velocity and distance
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Asked by asjadhav2003 | 24 Mar, 2020, 21:43: PM
answered-by-expert Expert Answer
Position vector as function of time t is given by, begin mathsize 14px style r with rightwards arrow on top equals space stack r subscript o with rightwards arrow on top space left parenthesis space 1 space minus a space t space right parenthesis space t end style ........................(1)
at t = 0, we have begin mathsize 14px style r with rightwards arrow on top end style = 0  i.e. starting position,
we see that when t = 1/a , we get begin mathsize 14px style r with rightwards arrow on top end style = 0 , i.e., starting point is reached at t = 1/a
velocity dbegin mathsize 14px style r with rightwards arrow on top end style/dt is obtained by differentiating eqn.(1),   dbegin mathsize 14px style r with rightwards arrow on top end style/dt = begin mathsize 14px style stack r subscript o with rightwards arrow on top space left parenthesis space 1 space minus space 2 space a space t space right parenthesis end style  .....................(2)
velocity when it is returning to statring point is obtained by substituting, t = 1/a   , i.e., dbegin mathsize 14px style r with rightwards arrow on top end style/dt = - begin mathsize 14px style stack r subscript o with rightwards arrow on top end style
It can be seen from eqn.(2) , initially velocity starts with begin mathsize 14px style stack r subscript o with rightwards arrow on top end style at t = 0 , then keep on decreasing, becoming zero at t = 1/(2a),
reversing the direction afterwards and finally reaches the starting point with velocity - begin mathsize 14px style stack r subscript o with rightwards arrow on top end style .
position vector at t=1/2a is given by, begin mathsize 14px style r with rightwards arrow on top end style = begin mathsize 14px style stack r subscript o with rightwards arrow on top end style / (4a)
Distance covered with negative velocity is also same . Hence total distance covered = begin mathsize 14px style stack r subscript o with rightwards arrow on top end style / (2a)
Answered by Thiyagarajan K | 25 Mar, 2020, 08:27: AM

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