After the force is removed, what is the kinetic energy of the object?

Steps to Solve

1. Calculate the Acceleration Due to the Force

To find the acceleration, use Newton's second law: $$ F = m \cdot a $$ Where:

• $ F = 5.8 , \text{N} $
• $ m = 2.2 , \text{kg} $

Rearranging gives: $$ a = \frac{F}{m} = \frac{5.8 , \text{N}}{2.2 , \text{kg}} $$

2. Calculate the Resulting Acceleration

Now divide the force by the mass: $$ a = \frac{5.8}{2.2} = 2.636 , \text{m/s}^2 $$

3. Calculate the Final Velocity

Use the kinematic equation: $$ v_f = v_i + a \cdot t $$ First, we need to find the time it takes to travel 3.0 m. Using the equation: $$ d = v_i \cdot t + \frac{1}{2} a \cdot t^2 $$ Here:

• $ d = 3.0 , \text{m} $
• $ v_i = 2.0 , \text{m/s} $

We can substitute this to find $ t $: $$ 3.0 = 2.0 \cdot t + \frac{1}{2} \cdot 2.636 \cdot t^2 $$

Using the quadratic formula or numerical methods will yield $ t \approx 1.118 , \text{s} $.

Now use $ v_f $: $$ v_f = 2.0 + 2.636 \cdot 1.118 $$

4. Calculate the Final Velocity

Calculating this gives us: $$ v_f \approx 2.0 + 2.944 \approx 4.944 , \text{m/s} $$

5. Calculate the Kinetic Energy

Finally, apply the kinetic energy formula: $$ KE = 0.5 \cdot m \cdot v_f^2 $$ Substituting the values: $$ KE = 0.5 \cdot 2.2 \cdot (4.944)^2 $$

Calculating this will give you the kinetic energy.

6. Calculate the Kinetic Energy Value

Calculating the final value: $$ KE = 0.5 \cdot 2.2 \cdot 24.44 \approx 26.87 , \text{J} $$

Therefore, rounding to the nearest whole number gives: $$ KE \approx 27 , \text{J} $$