Quadratic function and equation in one variable

Question

A particle moves along a straight line through a fixed point O. The speed, v ms^-1, is given by v =2t² - 9t + 16, where t is the time in seconds after the particle leaves the fixed point O. Find the values of t when the speed of the particle is

6 ms^-1.

Answer 1

Given function v = 2t² - 9t + 16

and we want t when v = 6 then

6 = 2t² - 9t + 16

=> 2t² - 9t + 10 = 0

=> (2t - 5)(t - 2) = 0

=> 2t - 5 = 0 and t - 2 = 0

hence v = 6 ms^-1 when t = 2 seconds and t = 2.5 seconds