Question

An object's motion is represented by the x vs. t graph shown below Hint: Velocity is the slope of x vs. t graph, and acceleration is slope of v vs. t graph. 130 points: 5 points each r (s) t (a) a. Draw the corresponding v vs. t graph on the axes provided. b. Draw the corresponding a vs. t graph on the axes provided. c. At what times is the position a maximum (most positive)? At those times, is the velocity a maximum, minimum, or zero? At those times, is the acceleration a maximum, minimum, or zero? d. At what times is the position a minimum (most negative)? At those times, is the velocity a maximum, minimum, or zero? At those times, is the acceleration a maximum, minimum, or zero? At what times is velocity a maximum (most positive)? At those times, what is the position of the object? Give a simple relationship between the sign of the position and the sign of the e. f. acceleration at the same instant of time.

Answer 1

5. An object's motion is represented by the x vs. t graph which can be shown below.

(a) Draw the corresponding v vs. t graph on the axes provided.

(b) Draw the corresponding a vs. t graph on the axes provided.

(c) At what time's is the position a maximum (most positive)?

$\Rightarrow$ At t = 1.5 sec and t = 3.5 sec, we get maximum position.

(d) At what time's is the position a minimum (most negative)?

$\Rightarrow$ At t = 0.5 sec and t = 2.5 sec, we get minimum position.

6. An object is attached to a spring and set into motion, oscillating vertically.

Which of the following statements is true regarding the motion of the object at the lowest point of its oscillation?

$\Rightarrow$ The object's velocity is equal to zero and displacement is a maximum.

Option (b) : it will be correct.

Explanation : When an object is oscillating in the vertical direction, then its maximum speed occurs when an object is at the equilibrium point. In simple harmonic motion, the magnitude of an acceleration of a body is always directly proportional to its displacement. The displacement in simple harmonic motion is a maximum, when the velocity is zero.