Question

A position-time graph for a particle moving along the x axis is shown in the figure. The divisions along the horizontal axis represent 1.75 s and the divisions along the vertical axis represent 4.0 m.

(a) Find the average velocity in the time interval t = 5.25 s to t = 14.00 s.

(b) Determine the instantaneous velocity at t = 7.00 s (where the tangent line touches the curve) by measuring the slope of the tangent line shown in the graph.

Answer 1

Question #80947, Physics / Other

A position-time graph for a particle moving along the $x$ axis is shown in the figure. The divisions along the horizontal axis represent 1.75 s and the divisions along the vertical axis represent 4.0 m.

(a) Find the average velocity in the time interval $t = 5.25$ s to $t = 14.00$ s.

(b) Determine the instantaneous velocity at $t = 7.00$ s (where the tangent line touches the curve) by measuring the slope of the tangent line shown in the graph.

Solution

a)

$$v _ {a v} = \frac {\Delta x}{\Delta t} = (4. 0) \frac {2 - 8}{1 4 - 5 . 2 5} = - 2. 7 4 \frac {m}{s}.$$

b)

$$v (7) = \frac {4 . 0}{1 . 7 5} \frac {0 - 1 3}{7 - 0} = - 4. 2 4 \frac {m}{s}.$$

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