A 1000kg car accelerate from rest to 20m/s in 10s what is the average power
Answer (2)
Answer:The average power developed by the car is 20000 W.Mass of the car: [tex]\(m=1000\text{\ kg}\) [/tex]Initial velocity: [tex]\(v_{i}=0\text{\ m/s}\)[/tex]Final velocity: [tex]\(v_{f}=20\text{\ m/s}\)[/tex]Time taken: [tex]\(t=10\text{\ s}\) [/tex]Kinetic energy formula: [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \(KE=\frac{1}{2}mv^{2}\) [/tex]Power is the rate of change of energy: [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \(P=\frac{\Delta E}{\Delta t}\)[/tex]Step 1 . Calculate the initial kinetic energy [tex]\(KE_{i}=\frac{1}{2}mv_{i}^{2}\)[/tex][tex]\(KE_{i}=\frac{1}{2}(1000\text{\ kg})(0\text{\ m/s})^{2}\) [/tex][tex]\(KE_{i}=0\text{\ J}\) [/tex]Step 2 . Calculate the final kinetic energy [tex]\(KE_{f}=\frac{1}{2}mv_{f}^{2}\)[/tex][tex]\(KE_{f}=\frac{1}{2}(1000\text{\ kg})(20\text{\ m/s})^{2}\)[/tex][tex]KE_{f}=\frac{1}{2}(1000\text{\ kg})(400\text{\ m}^{2}/\text{s}^{2})\)[/tex][tex]\(KE_{f}=200000\text{\ J}\)[/tex]Step 3 . Calculate the change in kinetic energy [tex]\(\Delta KE=KE_{f}-KE_{i}\)[/tex][tex]\(\Delta KE=200000\text{\ J}-0\text{\ J}\)[/tex][tex]\(\Delta KE=200000\text{\ J}\) [/tex]Step 4 . Calculate the average power [tex]\(P_{avg}=\frac{\Delta KE}{t}\)[/tex][tex]\(P_{avg}=\frac{200000\text{\ J}}{10\text{\ s}}\)[/tex][tex]\(P_{avg}=20000\text{\ W}\)[/tex]
To find the average power, we need to calculate the work done and then divide it by the time taken.First, let's find the kinetic energy (work done) using the formula:Kinetic Energy (KE) = 0.5 × m × v²where m = 1000 kg, v = 20 m/sKE = 0.5 × 1000 × (20)²= 0.5 × 1000 × 400= 200,000 JThe car starts from rest, so the initial kinetic energy is 0. The work done is equal to the final kinetic energy.Average Power (P) = Work done / Time taken= 200,000 J / 10 s= 20,000 W= 20 kWSo, the average power is 20 kW.
