A cart starts at rest at the origin of an x-axis and experiences the following…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A cart starts at rest at the origin of an x-axis and experiences the following piece-wise constant acceleration.
• From t = 0 s to t = 2 s: a = +3.0 m/s².
• From t = 2 s to t = 5 s: a = 0 m/s².
• From t = 5 s to t = 8 s: a = –2.0 m/s².
Answer the questions that follow. Assume motion is along the +x direction and neglect any friction.
(a) Determine the cart’s instantaneous velocity at t = 2 s, 5 s, and 8 s.
(b) Using the values found in part (a), sketch an accurately scaled velocity–time graph for 0 s ≤ t ≤ 8 s.
(c) Calculate the cart’s position at t = 2 s, 5 s, and 8 s.
(d) Based on your results, sketch a qualitative position–time graph for the full 8-s interval, clearly indicating where the graph is concave upward, linear, and concave downward.
(e) From your velocity graph, determine the exact time (to the nearest 0.1 s) at which the cart reverses direction. Justify your answer without algebraic integration.