Question35. Do this problem on a worksheet. Both car A and car B leave school when a clock reads zero. Car A travels at a constant , and car B travels at a constant . a. Draw a position-time graph showing the motion of both cars. b. How far are the two cars from school when the clock reads 2.0 h ? Calculate the distances using the equation for motion and show them on your graph. c. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph.
Studdy Solution
STEP 1
1. Car A travels at a constant speed of .
2. Car B travels at a constant speed of .
3. Both cars leave the school at the same time when the clock reads zero.
4. We need to draw a position-time graph for both cars.
5. We need to calculate the distance each car has traveled after 2 hours.
6. We need to determine when each car passes a gas station 120 km from the school.
STEP 2
1. Draw the position-time graph for both cars.
2. Calculate the distance each car has traveled after 2 hours.
3. Determine the time each car passes the gas station.
STEP 3
Draw the position-time graph for both cars.
- On the graph, the x-axis represents time (in hours) and the y-axis represents position (in kilometers).
- For Car A, plot a line starting from the origin with a slope representing its speed, .
- For Car B, plot a line starting from the origin with a slope representing its speed, .
STEP 4
Calculate the distance each car has traveled after 2 hours using the equation for motion: .
- For Car A:
$ \text{Distance}_A = 75 \, \text{km/h} \times 2 \, \text{h} = 150 \, \text{km}
\]
- For Car B:
$ \text{Distance}_B = 85 \, \text{km/h} \times 2 \, \text{h} = 170 \, \text{km}
\]
- Mark these distances on the graph at .
STEP 5
Determine the time each car passes the gas station 120 km from the school using the equation for motion: .
- For Car A:
$ \text{Time}_A = \frac{120 \, \text{km}}{75 \, \text{km/h}} = 1.6 \, \text{h}
\]
- For Car B:
$ \text{Time}_B = \frac{120 \, \text{km}}{85 \, \text{km/h}} \approx 1.41 \, \text{h}
\]
- Mark these times on the graph where each car passes the 120 km mark.
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