Math Problem Statement
A position-time graph for a particle moving along the x axis is shown in the figure below. A coordinate plane has a horizontal axis labeled t (s) and a vertical axis labeled x (m). There are two curves graphed on the plane.
The first is a straight line which runs from (0,13.3) to (3.5,0). The second is a curve which begins at (1,11), moves down and to the right with a slope that becomes gradually less steep until it is horizontal at approximately (4,2), then moves upward and to the right with an increasing slope until it ends at approximately (6.5,7).
The two curves meet at approximately (2,6.0). (a) Find the average velocity in the time interval t = 1.00 s to t = 3.50 s. (Indicate the direction with the sign of your answer.) m/s
(b) Determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph. (Note that t = 2.00 s is where the tangent line touches the curve. Indicate the direction with the sign of your answer.) m/s
(c) At what value of t is the velocity zero? s
Solution
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Math Problem Analysis
Mathematical Concepts
Kinematics
Velocity
Position-Time Graphs
Tangents
Slope
Average Velocity
Instantaneous Velocity
Formulas
v_avg = Δx / Δt
Instantaneous velocity = slope of tangent line
Theorems
Concept of average velocity
Concept of instantaneous velocity and tangent slopes
Suitable Grade Level
Grades 9-11