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