Sketch the acceleration graph on the graph sheet Since acceleration is the deriv

Question

Sketch the acceleration graph on the graph sheet Since acceleration is the derivative of velocity, should the velocity graph be curvy or straight? Based on acceleration, should the velocity graph be slanted upwards or slanted downwards? Explain, (using the power rule for derivatives may help) Now think about the relationship between the velocity and position graph. Because velocity is the derivative of position, what kind of polynomial should the position function be? Explain. Go back to your graph sheet and make your graphs more accurate, based on the thinking you have done. Record these graphs in the "updated" column. In this lab, we've dealt with three functions that are related to one another as rates of change. Position is the original function. Velocity is the rate of change in position. Acceleration is the rate of change in velocity. If f(x) is the position function, then f'(x) is the velocity function and f"(x) is the acceleration function.

Explanation / Answer

7. i) if velocity vs time graph is straight line then acceleration is constant

   ii) if the velocity graph is curved , accleration varies with the time.

iii) as the slope of velocity gets steeper , acceleration gets larger, i.e. velocity changes more rapidly.

now since acceleration is the derivative of velocity, the polynomial function which denotes acceleration will be one degree lesser than the velocity polynomial function. for example if the velocity function is quadratic polynomial, acceleration function will be a linear polinomial.but if velocity function is of greater than second degree polynomial function, accleration wont be linear in that case.

8. since the velocity is the derivative of the position polynomial function it will be of one degree lesser polynomial function that that of the position function.

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