8.01SC | Fall 2016 | Undergraduate
Classical Mechanics
Week 1: Kinematics

## 2.3 Worked Example - Acceleration from Position

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A runner travels along the x-axis, and at time $$\displaystyle t=0$$ is at the origin. The $$\displaystyle x$$-component of the runner’s position with respect to the origin is given by:

$$\displaystyle x(t)=bt^2$$

where $$\displaystyle b$$ is a positive constant.

(Part a) What are the units of the constant $$\displaystyle b$$? Express your answer in terms of m for meter and s for seconds.

(Part b) Find $$\displaystyle v(t)$$, the $$\displaystyle x$$-component of the runner’s velocity as a function of time.

(Part c) Find $$\displaystyle a(t)$$, the $$\displaystyle x$$-component of the runner’s acceleration as a function of time.

(Part d) Do a plot of $$\displaystyle x(t)$$, $$\displaystyle v(t)$$ and $$\displaystyle a(t)$$ vs. time.

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