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The acceleration of a particle is given ...

The acceleration of a particle is given by `a=t^3-3t^2+5`, where a is in `ms^-2` and t is in second. At `t=1s`, the displacement and velocity are `8.30m` and `6.25ms^-1`, respectively. Calculate the displacement and velocity at `t=2s`.

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To solve the problem step-by-step, we will first find the velocity function by integrating the acceleration function, and then we will find the displacement function by integrating the velocity function. Finally, we will evaluate both functions at \( t = 2 \) seconds. ### Step 1: Given Information The acceleration of the particle is given by: \[ a(t) = t^3 - 3t^2 + 5 \] At \( t = 1 \) second, the displacement \( x(1) = 8.30 \, \text{m} \) and the velocity \( v(1) = 6.25 \, \text{m/s} \). ...
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Knowledge Check

  • The position of an object moving along x-axis is given by x=a +bt^(2) , where a=8.5 m and b=2.5 ms^(-2) and (t) is measured in seconds. What is the velocity at t=1= 0 s and t=2.0 s? What is the average velocity between t=2.0s and t=4.0 s ? a) 5 m/s b) 10 m/s c) 15 m/s d) 20 m/s

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    B
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    C
    ` 15 m s^(-1)`
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