you travel down the highways, starting from rest. You travel for 2 hours at a speed of 105 km/h. then you stop and eat your lunch for 30 minutes. Then you travel for 1.5 hours at 75km/hr. Make a distance vs time graph of this motion.
To make a distance vs time graph of this motion, we need to understand the distances traveled during specific time intervals.
First, let's calculate the distances traveled during each leg of the journey:
1. For the first 2-hour leg at a speed of 105 km/h, the distance covered can be calculated using the formula:
Distance = Speed × Time
Distance = 105 km/h × 2 hours = 210 km
2. After that, a 30-minute lunch break is taken, which is equivalent to 0.5 hours.
3. Finally, during the last leg of 1.5 hours at a speed of 75 km/h, the distance can be calculated as:
Distance = Speed × Time
Distance = 75 km/h × 1.5 hours = 112.5 km
Now, let's create the distance vs time graph:
- On the x-axis (horizontal axis), we will represent time in hours.
- On the y-axis (vertical axis), we will represent distance in kilometers.
Using the calculated distances, we can plot the following points:
1. Time = 0 hours, Distance = 0 km (starting point)
2. Time = 2 hours, Distance = 210 km (end of the first leg)
3. Time = 2.5 hours, Distance = 210 km (pause during lunch)
4. Time = 4 hours, Distance = 322.5 km (end of the journey)
Connecting these points will form the distance vs time graph, which will have two line segments:
- A straight line segment with a slope of 105 km/h representing the first leg of the journey from 0 to 2 hours.
- Another straight line segment with a slope of 75 km/h representing the second leg of the journey from 2.5 to 4 hours.
The graph will show an initial steep incline followed by a horizontal line during the lunch break, and then a smaller incline until the end of the journey.