Math Problem Statement
The displacement (in meters) of a particle moving in a straight line is given by s=t^2-6t+19, where t is measured in seconds.
(A) (i) Find the average velocity over the time interval [3,4] (ii) Find the average velocity over the time interval [3.5,4] (iii) Find the average velocity over the time interval [4,5] (iv)Find the average velocity over the time interval [4,4.5]
(B) Find the instantaneous velocity when t=4
Units must be in meters per second Please list out all the answers in a visible readable format
Solution
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Math Problem Analysis
Mathematical Concepts
Kinematics
Calculus
Derivatives
Average Velocity
Instantaneous Velocity
Formulas
Average velocity formula: v_avg = (s(t2) - s(t1)) / (t2 - t1)
Instantaneous velocity formula: v(t) = ds/dt
Theorems
Definition of average velocity as the change in displacement over time
Definition of instantaneous velocity as the derivative of displacement
Suitable Grade Level
Grades 11-12
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