Question

the following graph represents the motion of a cyclist. what is the cyclists instantaneous velocity at t = 10 seconds?

Explanation:

Step1: Recall the formula for velocity

Velocity \(v=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time.

Step2: Identify two points on the line at \(t = 10\) seconds

Looking at the graph, we can take two points on the line segment where \(t = 10\) seconds lies. Let's take \((8,5.5)\) and \((13,0)\)

Step3: Calculate \(\Delta x\) and \(\Delta t\)

\(\Delta x=x_2 - x_1=0 - 5.5=- 5.5\) m, \(\Delta t=t_2 - t_1=13 - 8 = 5\) s

Step4: Calculate the velocity

\(v=\frac{\Delta x}{\Delta t}=\frac{-5.5}{5}=-1.1\) m/s

Answer:

\(-1.1\) m/s