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A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity
becomes 40 m/s towards north. The average acceleration of the body is
becomes 40 m/s towards north. The average acceleration of the body is
- a)5 m/s2
- b)1 m/s2
- c)7 m/s2
- d)3 m/s2
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem
A body initially moves with a velocity of 30 m/s towards the east, and after 10 seconds, its velocity changes to 40 m/s towards the north. We need to find the average acceleration during this time interval.
Initial and Final Velocities
- Initial Velocity (u): 30 m/s (East)
- Final Velocity (v): 40 m/s (North)
Vector Representation
- Represent the initial velocity as a vector: u = 30 i (where i is the unit vector in the east direction).
- Represent the final velocity as a vector: v = 40 j (where j is the unit vector in the north direction).
Change in Velocity
- The change in velocity (Δv) can be calculated as:
Δv = v - u = (0 i + 40 j) - (30 i + 0 j) = -30 i + 40 j
Magnitude of Change in Velocity
- The magnitude of the change in velocity can be calculated using the Pythagorean theorem:
|Δv| = √((-30)² + (40)²) = √(900 + 1600) = √2500 = 50 m/s
Average Acceleration Calculation
- Average acceleration (a) is given by the formula:
a = Δv / Δt
- Here, Δt = 10 seconds.
- Therefore, the average acceleration is:
a = 50 m/s / 10 s = 5 m/s²
Conclusion
The average acceleration of the body is 5 m/s², which corresponds to option 'a'.
A body initially moves with a velocity of 30 m/s towards the east, and after 10 seconds, its velocity changes to 40 m/s towards the north. We need to find the average acceleration during this time interval.
Initial and Final Velocities
- Initial Velocity (u): 30 m/s (East)
- Final Velocity (v): 40 m/s (North)
Vector Representation
- Represent the initial velocity as a vector: u = 30 i (where i is the unit vector in the east direction).
- Represent the final velocity as a vector: v = 40 j (where j is the unit vector in the north direction).
Change in Velocity
- The change in velocity (Δv) can be calculated as:
Δv = v - u = (0 i + 40 j) - (30 i + 0 j) = -30 i + 40 j
Magnitude of Change in Velocity
- The magnitude of the change in velocity can be calculated using the Pythagorean theorem:
|Δv| = √((-30)² + (40)²) = √(900 + 1600) = √2500 = 50 m/s
Average Acceleration Calculation
- Average acceleration (a) is given by the formula:
a = Δv / Δt
- Here, Δt = 10 seconds.
- Therefore, the average acceleration is:
a = 50 m/s / 10 s = 5 m/s²
Conclusion
The average acceleration of the body is 5 m/s², which corresponds to option 'a'.
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