Final answer:
The instantaneous velocity of an object whose position is given by x=2t² -6.7t at t=3.5 seconds is 7.3 m/s, calculated by taking the derivative of the position function and then evaluating it at the given time.
Step-by-step explanation:
To find the instantaneous velocity of an object when its position as a function of time is given by x=2t² -6.7t, where x and t are in SI units, we need to take the derivative of the position function with respect to time. This derivative represents the velocity function v(t).
The derivative of the position function x=2t² -6.7t with respect to time t is v(t) = d/dt(2t² -6.7t) = 4t - 6.7. To find the instantaneous velocity at t=3.5 seconds, we substitute 3.5 for t in the velocity function:
v(3.5) = 4(3.5) - 6.7 = 14 - 6.7 = 7.3 m/s.
Therefore, the instantaneous velocity of the object at t=3.5 seconds is 7.3 m/s.