graphical differentiation

Question

Position x (m) vs time t (s) graph of a particle is a parabola opening upward: x = 2 + 3t + t². Find velocity at t = 4 s.

RankGuru · Accepted Answer

1. **Relationship**: Instantaneous velocity is the time derivative of the position function: $v(t) = \frac{dx}{dt}$.
2. **Differentiate**: For $x(t) = 2 + 3t + t^2$:
   - $\frac{d}{dt}(2) = 0$
   - $\frac{d}{dt}(3t) = 3$
   - $\frac{d}{dt}(t^2) = 2t$
3. **Isolate v**: $v(t) = 3 + 2t$.
4. **Evaluate at point**: For $t = 4$ s:
   - $v(4) = 3 + 2(4) = 3 + 8 = 11$ m/s.
5. **Result**: The velocity at $4$ seconds is **$11$ m/s**.

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graphical differentiation

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