Graph slopes and areas Transitional Reasoning Practice

Questions

1. 1.

   A sensor on a straight test track records data for an electric cart across two consecutive motion stages. During Stage 1, spanning from t = 0 s to t = 5 s, the cart's position-time graph is a straight line rising from x = 10 m to x = 40 m. During Stage 2, from t = 5 s to t = 9 s, the cart undergoes a constant acceleration of -3 m/s² as represented on its acceleration-time graph. Based on the slope of the position-time graph and the area bounded by the acceleration-time graph, what are the cart's velocity at t = 5 s and its velocity at t = 9 s, respectively?

   • A) +8 m/s and -4 m/s
   • B) +6 m/s and +18 m/s
   • C) +6 m/s and -6 m/s
   • D) +30 m/s and +18 m/s
2. 2.

   A sensor-equipped cart travels along a straight track, and its motion is tracked on a velocity-time graph. Over an $8\text{ s}$ interval, the cart's velocity changes uniformly from $-4\text{ m/s}$ to $+12\text{ m/s}$. A student is tasked with finding the cart's acceleration from the slope of the graph and its net displacement from the area bounded by the graph line and the time axis. Which pair of values correctly represents the cart's acceleration and net displacement during this $8\text{ s}$ interval?

   • A) Acceleration: $1\text{ m/s}^2$; Net displacement: $40\text{ m}$
   • B) Acceleration: $2\text{ m/s}^2$; Net displacement: $40\text{ m}$
   • C) Acceleration: $2\text{ m/s}^2$; Net displacement: $32\text{ m}$
   • D) Acceleration: $1\text{ m/s}^2$; Net displacement: $32\text{ m}$

Answers and step-by-step solutions appear after you finish the test.