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Acceleration of a particle is given by ...

Acceleration of a particle is given by
` a= 3t^(2)+2t +1`
Where t is time . Find
(i) its velocity at time t assuming velocity to be 10 m/s at t = 0.
(ii) its position at time t assuming that the particle is at origin at t = 0.
(iii) What is the average speed of the particle in the duration t = 0 to t = 1s?
(iv) What is the average acceleration of the particle in the duration t = 0 to t = 1s?

Text Solution

AI Generated Solution

To solve the problem step by step, we will address each part of the question sequentially. ### Given: The acceleration of the particle is given by: \[ a(t) = 3t^2 + 2t + 1 \] ### (i) Finding Velocity at Time \( t \) ...
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Knowledge Check

  • A particle's position as a function of time is described as y (t) = 2t^(2) + 3t + 4 . What is the average velocity of the particle from t = 0 to t = 3 sec ?

    A
    3 m/sec
    B
    6 m/sec
    C
    9 m/sec
    D
    12 m/sec

  • Position of a particle at any instant is given by x = 3t^(2)+1 , where x is in m and t in sec. Its average velocity in the time interval t = 2 sec to t = 3 sec will be :

    A
    `15 m//s`
    B
    `12 m//s`
    C
    `18 m//s`
    D
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  • For a particle moving in a straight line, the displacement of the particle at time t is given by S=t^(3)-6t^(2) +3t+7 What is the velocity of the particle when its acceleration is zero?

    A
    `- 9 ms^(-1)`
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