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The position of object moving along an x...

The position of object moving along an x-axis is given by `x=3t-4t^(2)+t^(3)`, where x is in meters and t in seconds. Find the position of the object at the following values of t : (i) 2s, (ii) 4s, (iii) What is the object's displacement between t = 0 s and t = 4 s ? and (iv) What is its average vvelocity for the time interval from t = 2 s to t = 4 ?

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To solve the problem step by step, we will follow the instructions given in the question. ### Given: The position of the object is given by the equation: \[ x(t) = 3t - 4t^2 + t^3 \] where \( x \) is in meters and \( t \) is in seconds. ### Step 1: Find the position of the object at \( t = 2 \) seconds. ...
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Knowledge Check

  • The displacement of a particle moving in a straight line, is given by s = 2t^2 + 2t + 4 where s is in metres and t in seconds. The acceleration of the particle is.

    A
    `2 m//s^2`
    B
    `4 m//s^2`
    C
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    D
    `8 m//s^2`

  • The position of a particle moving on the x-axis is given by x=t^(3)+4t^(2)-2t+5 where x is in meter and t is in seconds (i) the velocity of the particle at t=4 s is 78 m//s (ii) the acceleration of the particle at t=4 s is 32 m//s^(2) (iii) the average velocity during the interval t=0 to t=4 s is 30 m//s (iv) the average acceleration during the interval t=0 to t=4 s is 20 m//s^(2)

    A
    (i), (ii)
    B
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    C
    (i), (ii), (iii)
    D
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  • The position of a body moving along x-axis at time t is given by x= (t^(2)-4t+6)m . The distance travelled by body in time interval t = 0 to t = 3 s is

    A
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    B
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    C
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