Question

1. the cyclist is moving at a steady speed and is currently at kilometer table to determine the cyclists position at various times. time (minutes) -6 -4 -2 0 position (km) -4 0 write and evaluate an expression for the position of the cyclis a 5 minutes b -10 minutes

Explanation:

Step1: Find the speed

The cyclist moves from position - 4 km at time 0 minutes to 0 km at time 4 minutes. Speed $v=\frac{\Delta x}{\Delta t}=\frac{0 - (-4)}{4-0}=1$ km/min.

Step2: Find position at 5 minutes

The initial position at $t = 0$ is $x_0=-4$ km. Using the formula $x=x_0+vt$, substituting $x_0=-4$, $v = 1$ and $t = 5$, we get $x=-4+1\times5=1$ km.

Step3: Find position at - 10 minutes

Using the same formula $x=x_0+vt$, with $x_0=-4$, $v = 1$ and $t=-10$, we get $x=-4+1\times(-10)=-14$ km.

Answer:

a. 1 km
b. - 14 km