1. Constant Velocity:
* Formula: Displacement (Δx) = Velocity (v) * Time (Δt)
* Explanation: If the velocity is constant, the displacement is simply the product of the velocity and the time interval.
2. Varying Velocity (Constant Acceleration):
* Formula: Displacement (Δx) = Initial Velocity (v₀) * Time (Δt) + (1/2) * Acceleration (a) * Time² (Δt²)
* Explanation: This formula is derived from the equations of motion for uniformly accelerated motion. It accounts for both the initial velocity and the acceleration acting over time.
3. Varying Velocity (Non-Constant Acceleration):
* Graphical Method:
* Area under the velocity-time curve: The displacement is represented by the area under the velocity-time curve.
* Divide the area into simpler shapes: If the curve is complex, you can divide the area into simpler shapes like rectangles and triangles, calculate their individual areas, and add them up to get the total displacement.
* Calculus Method:
* Integration: Displacement is the integral of the velocity function over the time interval.
* Formula: Δx = ∫v(t) dt, where v(t) is the velocity function and the integration is performed over the time interval.
Example:
Let's say a car starts from rest (v₀ = 0 m/s) and accelerates at 2 m/s² for 5 seconds.
Using the formula for constant acceleration:
* Δx = (0 m/s) * (5 s) + (1/2) * (2 m/s²) * (5 s)²
* Δx = 0 + 25 m
* Δx = 25 m
Therefore, the car's displacement after 5 seconds is 25 meters.
Remember:
* Displacement is a vector quantity, meaning it has both magnitude and direction.
* If the velocity is negative, the displacement will also be negative, indicating movement in the opposite direction.
* If the velocity-time graph has areas above and below the time axis, you need to consider both positive and negative displacements to get the net displacement.
