A point starts with the velocity 10 cm/sec and moves along a straight line with uniform acceleration 5cm/sec^2. How much time it takes to describe 80 cm?
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 6 seconds
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This interesting question is from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12
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Right option is (a) 4 seconds
To elaborate: Let us assume that the point takes t seconds to describe a distance 80 cm.
Then using the formula s = ut +1/2(ft^2) we get,
80 = 10*t + 1/2(5)(t^2)
Or 5t^2 + 20t – 160 = 0
Or t^2 + 4t – 32 = 0
Or (t – 4)(t + 8) = 0
Or t = 4 Or -8
Clearly, t = -8 is inadmissible.
Therefore, the required time = 4 seconds.