Questions: An object moves 30 m to the right while experiencing an acceleration. If its acceleration was 3 m / s^2 and its initial velocity was 10 m / s, what was the final velocity?

An object moves 30 m to the right while experiencing an acceleration. If its acceleration was 3 m / s^2 and its initial velocity was 10 m / s, what was the final velocity?

Transcript text: 10) An object moves 30 m to the right while experieficing an acceleration. If its acceleration was $3 \mathrm{~m} / \mathrm{s}^{2}$ and its initial velooity was $10 \mathrm{~m} / \mathrm{s}$, what was the final velocity?

Solution

Solution Steps

Step 1: Identify the Given Information

We are given:

Initial velocity, $ u = 10 \, \text{m/s} $
Acceleration, $ a = 3 \, \text{m/s}^2 $
Displacement, $ s = 30 \, \text{m} $

Step 2: Use the Kinematic Equation

To find the final velocity, $ v $, we use the kinematic equation: \[ v^2 = u^2 + 2as \]

Step 3: Substitute the Given Values

Substitute the given values into the equation: \[ v^2 = (10 \, \text{m/s})^2 + 2 \cdot 3 \, \text{m/s}^2 \cdot 30 \, \text{m} \] \[ v^2 = 100 + 180 \] \[ v^2 = 280 \]

Step 4: Solve for the Final Velocity

Take the square root of both sides to solve for $ v $: \[ v = \sqrt{280} \] \[ v \approx 16.7332 \, \text{m/s} \]