Data for the motion of an object are given in the following table. State whether the speed of the object is uniform or non-uniform. Find the average speed. | Time (s) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | | Distance (m) | 0 | 6 | 10 | 16 | 21 | 29 | 35 | 42 | 45 | 55 | 60 |
The speed of the object is non-uniform because it covers unequal distances in equal intervals of time.
According to the chapter, for uniform motion, an object covers equal distances in equal intervals of time. To determine if motion is uniform, we calculate the distance covered in each successive 10-second interval.
The distances covered in each 10-second interval are: 6 m, 4 m, 6 m, 5 m, 8 m, 6 m, 7 m, 3 m, 10 m, and 5 m, which are not equal.
Since these distances are unequal, the motion is non-uniform.
The average speed is calculated as total distance divided by total time: 60 m / 100 s = 0.6 m/s.
Explanation
The chapter states that for uniform motion, an object covers equal distances in equal intervals of time. To determine if motion is uniform, we calculate the distance covered in each successive 10-second interval. If these distances are unequal, the motion is non-uniform. Average speed is calculated as total distance divided by total time.
Solution Steps
Step 1: Calculate distance covered in each 10-second interval:
Step 2: 0-10s: 6 - 0 = 6 m
Step 3: 10-20s: 10 - 6 = 4 m
Step 4: 20-30s: 16 - 10 = 6 m
Step 5: 30-40s: 21 - 16 = 5 m
Step 6: 40-50s: 29 - 21 = 8 m
Step 7: 50-60s: 35 - 29 = 6 m
Step 8: 60-70s: 42 - 35 = 7 m
Step 9: 70-80s: 45 - 42 = 3 m
Step 10: 80-90s: 55 - 45 = 10 m
Step 11: 90-100s: 60 - 55 = 5 m
Step 12: Since distances (6, 4, 6, 5, 8, 6, 7, 3, 10, 5 m) are unequal, motion is non-uniform
Step 13: Calculate average speed: Total distance / Total time = 60 m / 100 s = 0.6 m/s