A low-friction laboratory cart moves along a straight horizontal track equipped with a motion sensor. The sensor records the cart’s velocity at 2.0s intervals, producing the following data:
Time t (s)
0
2
4
6
8
10
12
Velocity v (m/s)
0
1.5
3.0
3.0
3.0
1.5
0
Positive velocity indicates motion toward the +x direction.
a. Part 1: (a) Identify every time interval during which the net horizontal force on the cart is zero. Justify your choices.
b. Part 2: (b) For each interval identified in part (a), calculate the cart’s displacement.
c. Part 3: (c) Using the data in the table, construct a qualitative sketch of acceleration versus time for 0≤t≤12s. Clearly indicate numerical values where they can be determined from the data.
d. Part 4: (d) Determine the cart’s total displacement over the entire 12s period.
e. Part 5: (e) Explain how the features of your acceleration graph embody Newton’s first law for the intervals of zero net force and illustrate the transition to intervals with non-zero net force.