KINETIC AND POTENTIAL
1. You are running around a track at 5 m/s and then you increase your speed to 10 m/s.
what factor did you increase your kinetic energy?



Answer :

The kinetic energy (KE) of an object can be calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] where m is the mass of the object and v is its velocity. When you are running around a track, your kinetic energy is determined by your speed. Initially, you are running at an initial speed of 5 m/s, which we'll call \( v_i \). Then you increase your speed to 10 m/s, which we'll call \( v_f \). The initial kinetic energy, \( KE_i \), when you are running at 5 m/s is proportional to the square of your initial speed: \[ KE_i ∝ (v_i)^2 \] \[ KE_i ∝ (5)^2 \] \[ KE_i ∝ 25 \] After increasing your speed to 10 m/s, your final kinetic energy, \( KE_f \), is proportional to the square of your final speed: \[ KE_f ∝ (v_f)^2 \] \[ KE_f ∝ (10)^2 \] \[ KE_f ∝ 100 \] To find the factor by which your kinetic energy increased, you would divide your final kinetic energy by your initial kinetic energy: \[ \text{Factor of Increase} = \frac{KE_f}{KE_i} \] Putting in the proportionality constants we have: \[ \text{Factor of Increase} = \frac{100}{25} \] \[ \text{Factor of Increase} = 4 \] So, when you increase your speed from 5 m/s to 10 m/s, you increase your kinetic energy by a factor of 4.