alculate the kinetic energies of (a) a 2.00*103-kg automobile moving at 100.0 km/h; (b) an 80.0-kg runner sprinting at 10.0 m/s; and (c) a 9.10 * 10-31-kg electron moving at 2.00 * 107 m/s.

(a) 7.72*10⁵ J

(b) 4000 J

(c) 1.82*10⁻¹⁶ J

Explanation:

Kinetic Energy: This can be defined energy of a body due to its motion. The expression for kinetic energy is given as,

Ek = 1/2mv² ... Equation 1

Where Ek = Kinetic energy, m = mass, v = velocity

(a)

For a moving automobile,

Ek = 1/2mv².

Given: m = 2.0*10³ kg, v = 100 km/h = 100 (1000/3600) m/s = 27.78 m/s

Substitute into equation 1

Ek = 1/2 (2.0*10³) (27.78²)

Ek = 7.72*10⁵ J

(b)

For a sprinting runner,

Given: m = 80 kg, v = 10 m/s

Substitute into equation 1 above,

Ek = 1/2 (80) (10²)

Ek = 40 (100)

Ek = 4000 J

(c)

For a moving electron,

Given: m = 9.10*10⁻³¹ kg, v = 2.0*10⁷ m/s

Substitute into equation 1 above,

Ek = 1/2 (9.10*10⁻³¹) (2.0*10⁷) ²

Ek = 1.82*10⁻¹⁶ J