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A particle moving with a uniform acceleration travels 24m and 64m in the first two consecutive intervals of 4 sec each. Its initial velocity is?
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A particle moving with a uniform acceleration travels 24m and 64m in t...
Uniform Acceleration


  • Given: Distance travelled in first two consecutive intervals = 24m and 64m, Time interval = 4 sec

  • Formula: Distance travelled = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)



Finding Acceleration


  • Acceleration is the rate of change of velocity with respect to time

  • Here, the particle is moving with a uniform acceleration

  • So, we can assume that the acceleration is constant throughout the motion

  • Using the formula, Distance = 0.5 * Acceleration * Time^2, we can find the acceleration as follows:



For first interval:


  • Distance = 24m

  • Time = 4 sec

  • Acceleration = (2 * Distance)/(Time^2) = (2 * 24)/(4^2) = 3 m/s^2



For second interval:


  • Distance = 64m

  • Time = 4 sec

  • Acceleration = (2 * Distance)/(Time^2) = (2 * 64)/(4^2) = 8 m/s^2



Finding Initial Velocity


  • Using the formula, Distance travelled = (Initial velocity * Time) + (0.5 * Acceleration * Time^2), we can find the initial velocity as follows:



For first interval:


  • Distance = 24m

  • Time = 4 sec

  • Acceleration = 3 m/s^2 (from above)

  • Initial velocity = (Distance - 0.5 * Acceleration * Time^2)/Time = (24 - 0.5 * 3 * 4^2)/4 = 3 m/s



For second interval:


  • Distance = 64m

  • Time = 4 sec

  • Acceleration = 8 m/s^2 (from above)

  • Initial velocity = (Distance - 0.5 * Acceleration * Time^2)/Time = (64 - 0.5 * 8 * 4^2)/4 = 8 m/s



Conclusion


  • The initial velocity of the particle is 3 m/s in the first interval and 8 m/s in the second interval.

Community Answer
A particle moving with a uniform acceleration travels 24m and 64m in t...
1m/s
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A particle moving with a uniform acceleration travels 24m and 64m in the first two consecutive intervals of 4 sec each. Its initial velocity is?
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