Final answer:
To find the instantaneous velocity of an object, take the derivative of the position function. The total distance traveled can be found by integrating the absolute value of the velocity function. Average acceleration is found by taking the derivative of the velocity function. The final position is obtained by evaluating the position function at the given time.
Step-by-step explanation:
a) The instantaneous velocity of an object moving along a line can be found by taking the derivative of the position function with respect to time. If the position function is denoted as x(t), then the instantaneous velocity function, v(t), can be calculated as v(t) = dx/dt.
b) The total distance traveled by the object can be determined by taking the integral of the absolute value of the velocity function over the given time interval. This will give the sum of all the displacements, regardless of direction.
c) Average acceleration can be calculated by taking the derivative of the velocity function with respect to time. If the velocity function is denoted as v(t), then the average acceleration, a_avg, can be calculated as a_avg = dv/dt.
d) The final position of the object can be determined by evaluating the position function at the given time.