Question

calculate the speed: speed in m/s position at t = 3h is: position at t = 2h is: position at t = 1h 20 min is:

Explanation:

Step1: Recall speed - distance - time formula

Speed $v=\frac{\Delta x}{\Delta t}$. From the graph, when $t = 3h$, $x = 1.5km$; when $t = 0h$, $x = 0km$. So $\Delta x=1.5 - 0=1.5km$ and $\Delta t = 3-0 = 3h$.

Step2: Calculate speed in km/h

$v=\frac{1.5km}{3h}=0.5km/h$.

Step3: Convert km/h to m/s

We know that $1km = 1000m$ and $1h=3600s$. So $v = 0.5\times\frac{1000m}{3600s}=\frac{500}{3600}m/s=\frac{5}{36}m/s\approx0.139m/s$.

Step4: Find position at $t = 3h$

From the graph, when $t = 3h$, the position $x = 1.5km$.

Step5: Find position at $t = 2h$

Since the motion is uniform (straight - line on $x - t$ graph), the speed $v = 0.5km/h$. Using $x=v\times t$, when $t = 2h$, $x=0.5km/h\times2h = 1km$.

Step6: Convert $1h\ 20min$ to hours

$1h\ 20min=1+\frac{20}{60}h=1+\frac{1}{3}h=\frac{4}{3}h$.

Step7: Find position at $t=\frac{4}{3}h$

Using $x = v\times t$ with $v = 0.5km/h$, $x=0.5km/h\times\frac{4}{3}h=\frac{2}{3}km\approx0.67km$.

Answer:

Speed in m/s: $\frac{5}{36}m/s$
Position at $t = 3h$: $1.5km$
Position at $t = 2h$: $1km$
Position at $t = 1h\ 20min$: $\frac{2}{3}km$