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A particle moves for 20 seconds with velocity 3 m/s, then moves with velocity 4 m/s for another 20 seconds, and finally moves with velocity 5 m/s for the next 20 seconds. What is the average velocity of the particle?
- a)3 m/s
- b)4 m/s
- c)4 m/s
- d)Zero
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A particle moves for 20 seconds with velocity 3 m/s, then moves with ...
Solution:
Given,
Velocity of the particle for the first 20 seconds = 3 m/s
Velocity of the particle for the next 20 seconds = 4 m/s
Velocity of the particle for the last 20 seconds = 5 m/s
Total time taken by the particle = 20 + 20 + 20 = 60 seconds
We need to find out the average velocity of the particle.
Formula to calculate the average velocity of the particle is given by:
Average velocity = Total displacement / Total time taken
As the motion of the particle is uniform, we can use the following formula to calculate the displacement of the particle:
Displacement = Velocity x Time
Let's calculate the displacement of the particle for each 20 seconds interval:
Displacement for the first 20 seconds = 3 m/s x 20 s = 60 m
Displacement for the next 20 seconds = 4 m/s x 20 s = 80 m
Displacement for the last 20 seconds = 5 m/s x 20 s = 100 m
Total displacement of the particle = 60 m + 80 m + 100 m = 240 m
Therefore, the average velocity of the particle is given by:
Average velocity = Total displacement / Total time taken
Average velocity = 240 m / 60 s
Average velocity = 4 m/s
Hence, the correct option is (b) 4 m/s.
Given,
Velocity of the particle for the first 20 seconds = 3 m/s
Velocity of the particle for the next 20 seconds = 4 m/s
Velocity of the particle for the last 20 seconds = 5 m/s
Total time taken by the particle = 20 + 20 + 20 = 60 seconds
We need to find out the average velocity of the particle.
Formula to calculate the average velocity of the particle is given by:
Average velocity = Total displacement / Total time taken
As the motion of the particle is uniform, we can use the following formula to calculate the displacement of the particle:
Displacement = Velocity x Time
Let's calculate the displacement of the particle for each 20 seconds interval:
Displacement for the first 20 seconds = 3 m/s x 20 s = 60 m
Displacement for the next 20 seconds = 4 m/s x 20 s = 80 m
Displacement for the last 20 seconds = 5 m/s x 20 s = 100 m
Total displacement of the particle = 60 m + 80 m + 100 m = 240 m
Therefore, the average velocity of the particle is given by:
Average velocity = Total displacement / Total time taken
Average velocity = 240 m / 60 s
Average velocity = 4 m/s
Hence, the correct option is (b) 4 m/s.
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Community Answer
A particle moves for 20 seconds with velocity 3 m/s, then moves with ...
Average velocity and instantaneous velocities have same value in a uniform motion. Average velocity is that uniform velocity with which the object will cover the same displacement in same interval of time as it does with its actual variable velocity during that time interval.
Here, total distance covered
= (3 m/s × 20 s) + (4 m/s × 20 s) + (5 m/s × 20 s)
= (60 + 80 + 100) = 240 m
Total time taken = 20 + 20 + 20
= 60 s
∴ Average velocity = 240/60 = 4m/s
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