Answer:
a.) a = F/m = 58 N / 28 kg = 2.07 m/s²
b.) v = u + at = 0 + 2.07 m/s² x 9 s = 18.63 m/s
c.) s = (u + v)/2 x t = (0 + 18.63 m/s)/2 x 9 s = 83.84 m
d.) KE = PE (1/2)mv² = mgh h = v² / (2g) = (18.63 m/s)² / (2 x 9.8 m/s²) = 17.64 m
e.) W = ΔKE W = (1/2)mv² - 0 W = (1/2)(28 kg)(18.63 m/s)² W = 4834 J
Step-by-step explanation:
(a) The biker’s acceleration can be found by using Newton’s second law of motion, which states that the net force on an object is equal to its mass times its acceleration. In this case, the net force is the pedaling force of 58 N, and the mass is 28 kg. Therefore, the acceleration is:
a = F/m = 58 N / 28 kg = 2.07 m/s²
(b) The biker’s final speed can be found by using the kinematic equation that relates initial speed, final speed, acceleration, and time. In this case, the initial speed is zero, the acceleration is 2.07 m/s^2, and the time is 9 s. Therefore, the final speed is:
v = u + at = 0 + 2.07 m/s² x 9 s = 18.63 m/s
(c) The distance covered by the biker can be found by using another kinematic equation that relates initial speed, final speed, acceleration, and distance. In this case, the initial speed is zero, the final speed is 18.63 m/s, and the acceleration is 2.07 m/s^2. Therefore, the distance is:
s = (u + v)/2 x t = (0 + 18.63 m/s)/2 x 9 s = 83.84 m
(d) The height of the hill that the biker can climb can be found by using the conservation of energy principle, which states that the total mechanical energy of a system remains constant if there are no non-conservative forces acting on it. In this case, we can assume that there are no friction or air resistance forces, so the mechanical energy of the biker consists of kinetic energy and gravitational potential energy. At the bottom of the hill, the biker has only kinetic energy, and at the top of the hill, he has only potential energy. Therefore, we can equate these two energies and solve for the height:
KE = PE (1/2)mv² = mgh h = v² / (2g) = (18.63 m/s)² / (2 x 9.8 m/s²) = 17.64 m
(e) The work done by the biker can be found by using the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work is done by the pedaling force of 58 N, and the change in kinetic energy is from zero to (1/2)mv^2. Therefore, the work is:
W = ΔKE W = (1/2)mv² - 0 W = (1/2)(28 kg)(18.63 m/s)² W = 4834 J
✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧