Question

use the diagram shown for problems 3 and 4.

1. the cyclist is moving at a steady speed and is currently at kilometer 0. complete the table to determine the cyclists position at various times.
2. write and evaluate an expression for the position of the cyclist at each time.

a 5 minutes
b -10 minutes

Explanation:

Step1: Find the speed

The cyclist moves from - 4 km at - 2 minutes to 0 km at 0 minutes. The change in position $\Delta x=0 - (-4)=4$ km and the change in time $\Delta t = 0-(-2)=2$ minutes. The speed $v=\frac{\Delta x}{\Delta t}=\frac{4}{2} = 2$ km/min.

Step2: Calculate positions for table

For $t=-6$ minutes: Using the formula $x = x_0+v\times t$, with $x_0 = 0$ (position at $t = 0$) and $v = 2$ km/min, $x=0+2\times(-6)=-12$ km.
For $t=-4$ minutes: $x=0 + 2\times(-4)=-8$ km.
For $t = 4$ minutes: $x=0+2\times4 = 8$ km.

Step3: Calculate positions for sub - questions

For part a ($t = 5$ minutes): Using the formula $x=x_0 + v\times t$ with $x_0 = 0$ and $v = 2$ km/min, $x=0+2\times5=10$ km.
For part b ($t=-10$ minutes): $x=0+2\times(-10)=-20$ km.

Answer:

Time (minutes)	-6	-4	-2	0	2	4

a. 10 km
b. -20 km