A driver travel from sunyani to Kumasi .The distance between the two cities is 30 km. After 60 mins, the driver stopped at Bechem which is 10km from sunyani 30mins later he continues to Kumasi in 60 mins. After resting for 30mins, he made a return journey in 120 minutes. Draw a distance time graph for the above information. From your graph: i) Find the speed from Bechem to Kumasi
To draw a distance-time graph, we need to plot the distance traveled at different points in time.
First, let's break down the journey and note the time and distance at each point:
- From Sunyani to Bechem: 60 minutes, 10 km
- From Bechem to Kumasi: 60 minutes, 20 km
- Resting time in Kumasi: 30 minutes
- Return journey from Kumasi to Bechem: 120 minutes, 20 km
- From Bechem to Sunyani: 60 minutes, 10 km
Now let's plot these points on a graph.
The x-axis represents time (in minutes) and the y-axis represents distance (in km).
Plot the following points:
- (60, 10) - Sunyani to Bechem
- (120, 20) - Bechem to Kumasi
- (180, 20) - Resting time in Kumasi
- (300, 0) - Return journey from Kumasi to Bechem
- (360, 10) - Bechem to Sunyani
Now connect the points with straight lines.
|
K +-------------------+
| /| |
| / | |
| / | |
| / | |
| / | |
| / | |
B +-------------------+
| | | |
| | | |
| |Resting| |
| | |time | |
S +---------------+
(0,0) 60 120 180 240 300
From the graph, we can see that the time taken from Bechem to Kumasi is 120 minutes, and the distance traveled is 20 km.
To find the speed, we use the formula:
Speed = Distance/Time
Speed = 20 km / 120 min = 1/6 km/min.
Therefore, the speed from Bechem to Kumasi is 1/6 km/min.
To draw the distance-time graph, we will use the following information:
- Sunyani to Bechem: 10 km, 60 mins
- Bechem to Kumasi: 20 km, 60 mins
- Resting time at Kumasi: 30 mins
- Return journey from Kumasi to Bechem: 20 km, 120 mins
First, let's plot the points on a graph:
1. Sunyani to Bechem (10 km, 60 mins):
- Point A: (0, 0)
- Point B: (60, 10)
2. Bechem to Kumasi (20 km, 60 mins):
- Point C: (60, 10)
- Point D: (120, 30)
3. Resting time at Kumasi (30 mins):
- Point E: (120, 30)
- Point F: (150, 30)
4. Return journey from Kumasi to Bechem (20 km, 120 mins):
- Point G: (150, 30)
- Point H: (270, 50)
Now, let's connect the plotted points on the graph:
- Line AB represents Sunyani to Bechem.
- Line CD represents Bechem to Kumasi.
- Line EF represents resting time at Kumasi.
- Line GH represents the return journey from Kumasi to Bechem.
The resulting distance-time graph would look like this:
|
| D __________ |
| / \ |
| / C|
| / B \|
|A_________________|
0 60 120 150 270
Now, to find the speed from Bechem to Kumasi, we can calculate the gradient of the line CD (Bechem to Kumasi).
The gradient is given by: slope = (change in distance)/(change in time)
Measured from the graph, the change in distance is 20 km (from C to D), and the change in time is 60 mins.
Therefore, the speed from Bechem to Kumasi is:
speed = (change in distance)/(change in time)
= 20 km / 60 mins
= 1/3 km/min or 20 km/hr