Distance Travelled When Particle Is Projected Upwards Using Initial Velocity And Time Calculator

Formula Used:

\[ \text{Distance Traveled Moving Upwards} = -\text{Initial Velocity} \times \text{Time} + \frac{1}{2} \times [g] \times \text{Time}^2 \]

Distance Traveled Moving Upwards:

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1. What Is The Distance Travelled When Particle Is Projected Upwards Using Initial Velocity And Time?

This calculation determines the vertical distance traveled by a particle projected upwards, accounting for gravitational acceleration. It's derived from kinematic equations of motion under constant acceleration.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ \text{Distance Traveled Moving Upwards} = -\text{Initial Velocity} \times \text{Time} + \frac{1}{2} \times [g] \times \text{Time}^2 \]

Where:

\( \text{Initial Velocity} \) — Starting velocity of the particle (m/s)
\( \text{Time} \) — Time elapsed (s)
\( [g] \) — Gravitational acceleration constant (9.80665 m/s²)

Explanation: The negative initial velocity term accounts for upward motion against gravity, while the positive acceleration term represents gravitational pull.

3. Importance Of Distance Calculation

Details: Calculating vertical distance traveled is essential in physics, engineering, and ballistics for predicting projectile motion, analyzing trajectories, and solving real-world problems involving vertical movement.

4. Using The Calculator

Tips: Enter initial velocity in m/s and time in seconds. Both values must be non-negative. The calculator will compute the vertical distance traveled during the specified time period.

5. Frequently Asked Questions (FAQ)

Q1: Why is the initial velocity term negative?
A: The negative sign indicates that upward motion is opposite to the direction of gravitational acceleration, which is conventionally taken as positive downward.

Q2: What happens if the calculated distance is negative?
A: A negative result indicates the particle has descended below its starting point, meaning it reached maximum height and started falling back down.

Q3: Does this formula account for air resistance?
A: No, this is an idealized formula that assumes no air resistance and constant gravitational acceleration.

Q4: Can this be used for any upward projection angle?
A: This specific formula calculates vertical distance only. For angled projections, vertical and horizontal components must be calculated separately.

Q5: What is the maximum height reached by the particle?
A: Maximum height occurs when vertical velocity becomes zero, calculated using \( h_{max} = \frac{u^2}{2g} \), where u is initial vertical velocity.