Question

problem 1. a cannonball has an initial velocity of 10 m/s. it reaches a final velocity of 12 m/s after traveling a displacement of 112 m. calculate the amount of time that the cannonball was in the air.
problem 2. an ice skater begins from rest and accelerates forwards at a rate of 0.6 m/s². determine their displacement after 18 seconds have passed.
problem 3. a beaver has an initial velocity of 2 m/s. it accelerates at a rate of 3 m/s² before reaching a final velocity of 11 m/s. calculate the displacement of the beaver.
problem 4. symir is decelerating at a rate of -0.7 m/s² before coming to a complete stop. if he travels a displacement of 95 m, calculate the amount of time that he was running.

Explanation:

Step1: Find acceleration

Use the formula \(v_{f}^{2}=v_{i}^{2}+2a\Delta x\).
Given \(v_{i} = 10\ m/s\), \(v_{f}=12\ m/s\), \(\Delta x = 112\ m\).
Substitute into the formula: \(12^{2}=10^{2}+2a\times112\).
\(144 = 100+224a\).
\(224a=144 - 100\).
\(224a = 44\).
\(a=\frac{44}{224}=\frac{11}{56}\ m/s^{2}\).

Step2: Calculate time

Use the formula \(v_{f}=v_{i}+at\).
Rearrange for \(t\): \(t=\frac{v_{f}-v_{i}}{a}\).
Substitute \(v_{i} = 10\ m/s\), \(v_{f}=12\ m/s\), \(a=\frac{11}{56}\ m/s^{2}\).
\(t=\frac{12 - 10}{\frac{11}{56}}\).
\(t=\frac{2\times56}{11}=\frac{112}{11}\approx10.18\ s\).

Answer:

The cannonball was in the air for approximately \(10.18\ s\).