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 \(\Delta x\) and \(\Delta t\) at \(t = 10\) s

Looking at the graph, at \(t=8\) s, \(x = 5.5\) m and at \(t = 12\) s, \(x=1\) m. So \(\Delta x=1 - 5.5=- 4.5\) m and \(\Delta t=12 - 8 = 4\) s.

Step3: Calculate the velocity

\(v=\frac{\Delta x}{\Delta t}=\frac{-4.5}{4}=-1.125\) m/s.

Answer:

\(-1.125\) m/s