Does a car’s kinetic energy change more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s? Explain.

Solution 10DQ Introduction We have to explain why the change in kinetic energy is more when velocity changes from 15 m/s to 20 m/s than when velocity changes from 10 m/s to 15 m/s, even though the change in velocity is same. Step 1 Suppose the mass of the car is m. Hence the the kinetic energy of the car, when the velocity is v = 10 m/s, v = 15 m/s and v = 20 m/s 1 2 3 are 1 1 2 E 1 mv2 12= m210 m/s) = (50 m /s )m 2 1 1 2 E 1 mv2 22= m215 m/s) = (112.5 m /s )m2 2 And 1 2 1 2 2 2 E 1 mv2 3 = m220 m/s) = (200 m /s )m