The displacement of a particle, moving in a straight line, is given by $s = 2t^2 + 2t + 4$ where $s$ is in met

Question

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:

Accepted Answer

1.  **Velocity ($v$):** Instantaneous velocity is defined as the rate of change of displacement with respect to time ($v = \frac{ds}{dt}$) .
    Given $s = 2t^2 + 2t + 4$.
    Differentiating with respect to $t$:
    $v = \frac{d}{dt}(2t^2 + 2t + 4) = 4t + 2$.
2.  **Acceleration ($a$):** Instantaneous acceleration is defined as the rate of change of velocity with respect to time ($a = \frac{dv}{dt}$) .
    Differentiating $v$ with respect to $t$:
    $a = \frac{d}{dt}(4t + 2) = 4$.
3.  **Result:** The acceleration is constant at $4 	ext{ m/s}^2$.

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