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# Help

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A position vs. time graph for a uniformly accelerating skateboarder riding down a ramp is shown below. What is the acceleration of the skateboarder?

Nov 14, 2021
edited by Guest  Nov 14, 2021

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Time 0    velo = 0     m/s

time  4    velo = 10

Change in velo / change in time = accel =    10 m/s  /  4 sec  == 2.5 m/s2

Nov 14, 2021
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What is the acceleration of the skateboarder?

Hello Guest!

The way_time_diagram shows the relationship of the skateboarder's way with time.

time  |   1    2    3    4   s

way  |    1   3    6   10  m

$$s=\dfrac{1}{2}t (t+1)$$

The functions of distance, speed and acceleration are linked to one another via their time derivatives.

$$\color{blue}way\\ s(t)\\ s(t)=\dfrac{1}{2}t (t+1)\ [m]$$         $$\color{blue}speed \\ v(t)= \dot s(t)\\ v(t)=\dfrac{2t+1}{2}\ [\frac{m}{s}]$$          $$\color{blue}acceleration \\ a(t)=\dot v(t)=\ddot s(t)\\ \color{blue}a(t)=1\ [\frac{m}{s^2}]\\$$

time              |     1   2      3     4   s

way              |     1    3     6    10  m

speed           |   1.5  2.5  3.5  4.5 m/s

acceleration |    1     1     1     1   m/s²

The acceleration of the skateboarder is continuous 1 m/s². !

Nov 15, 2021
edited by asinus  Nov 15, 2021