For a point starting at a point P and travelling along a straight line, time of travel is taken as t and the distance from P as s. The relation between s and t is found to be s = 12t – 2t2, there distances to the right are taken as positive numbers and to the left as negative numbers.
(i) Is the position of the point to the right or left of P, till 6 seconds?
(ii) Where is the position at 6 seconds?
(iii) After 6 seconds?
Here it is convenient to write 12t – 2t2 = 2t(6 – t).
s = 12t – 2t2
(i) when t = 6, s = 12×6-2(6)2
= 72-36×2
= 0
Thus, it is neither left nor right of point P.
(ii) s = 2t(6-t)
At t = 6s,
s = 2×6(6-6) = 0
Hence, it is at point P.
(iii) s = 12t- 2t2 it can have written as 2t(6-t)
After 6 seconds the term (6-t) will be negative
At t = 7 s = 2×7(6-7)
s = 14 ×-1
s = -14
At t = 8 s = 2×8(6-8)
s = 16× -2
s = -32
It will be left of point P after t = 6 seconds
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