integration for displacement

Question

Velocity of a particle varies as v = 4t (m/s). Find displacement in first 5 s (starts at origin).

RankGuru · Accepted Answer

1. **Principle**: Displacement is the integral of velocity over time: $s = \int v(t) dt$.
2. **Application**: For $v(t) = 4t$ from $t=0$ to $t=5$:
   - $s = \int_0^5 4t \, dt$
3. **Calculation**:
   - $s = [ 4 \cdot \frac{t^2}{2} ]_0^5$
   - $s = [ 2t^2 ]_0^5 = 2(5^2) - 2(0^2)$
   - $s = 2 	imes 25 = 50$ m.
4. **Conclusion**: The total displacement in $5$ seconds is **$50$ m**.

Rank Guru

integration for displacement

Select the correct option: