The distance time graph shows a cart moving at a straight path.
a. Describe the speed of the cart between:
1.) A and B - The cart is moving with constant speed for 10 seconds and it is now at rest for 20 seconds.
2.) B and C - The cart at rest for 20 seconds will now start moving with acceleration for 10 seconds.
3.) C and D - The cart starts to move with acceleration for 10 seconds.
b. What is the total distance traveled?
c. What is the average speed of the cart?
To answer these questions, we need to understand the information provided in the distance-time graph. Let's analyze each scenario step by step:
a.
1.) A and B - The distance-time graph shows that the cart is moving at a constant speed for 10 seconds and then comes to rest for 20 seconds. This means that the cart covers a certain distance during the 10 seconds it is moving and then doesn't move during the 20-second rest period.
2.) B and C - In this case, the graph indicates that the cart is at rest for 20 seconds and then starts moving with acceleration for 10 seconds. This implies that during the 20-second rest period, the cart covers zero distance, and then it starts covering a progressively increasing distance due to the acceleration during the next 10 seconds.
3.) C and D - The graph shows that the cart starts to move with acceleration for 10 seconds. This means that during this period, the cart is covering a distance that is increasing as time goes on.
b. To determine the total distance traveled, we need to calculate the sum of the distances covered in each section. Let's assign suitable labels to each segment of the graph:
|-----A-----|-----B-----|-----C-----|-----D-----|
The total distance can be calculated as:
Distance AB + Distance BC + Distance CD
Considering the information given for each segment, we can calculate the distances as follows:
Distance AB:
Since the cart is moving at a constant speed, the distance covered is given by the formula: Distance = Speed x Time.
Given that the cart moves at the same speed for 10 seconds, we multiply the speed by the time to get the distance.
Distance BC:
During the 20-second rest period, the cart doesn't cover any distance, so the distance is zero.
Distance CD:
The cart starts to move with acceleration for 10 seconds. To calculate the distance covered during this acceleration phase, we need more information, such as the acceleration rate or the final speed. Without this information, we cannot calculate the exact distance.
c. The average speed of the cart can be calculated by dividing the total distance traveled (calculated in part b) by the total time taken. So, we need to add up the times for each segment:
Time AB + Time BC + Time CD
The average speed can then be calculated as:
Average speed = Total distance / Total time