Question

The distance S object travel under the influence of gravity in time t seconds is given by S(t) = `1/2` gt² + at + b where, (g is the acceleration due to gravity), a, b are constant. Verify whether the function S(t) is one-one or not.

Answer 1

S(t) = `1/2` gt² + at + b 

Let t be 1, 2, 3, ………, seconds

S(1) = `1/2` g(1²) + a(1) + b = `1/2` g + a + b

S(2) = `1/2` g(2²) + a(2) + b = 2g + 2a + b

Yes, for every different value of t, there will be different values as images.

And there will be different pre-images for the different values of the range.

Therefore it is the one-one function.