45. Review. Two constant forces act on an object of mass m = QC 5.00 kg moving in the xy plane as shown in Figure P7.45. Force F, is 25.0 N at 35.0°, and force F, is 42.0 N at 150°. At time t = 0, the object is at the origin and has velocity (4.00i + 2.50j) m/s. (a) Express the two forces in unit-vector notation. Use unit-vector notation for your other answers. (b) Find the total force exerted on the object. (c) Find the object's acceleration. Now, considering the instant t= 3.00 s, find (d) the object's velocity, (e) its position, () its kinetic energy from fmu, and (g) its kinetic energy from 150 m + EF - A7. (h) What conclusion can you draw by comparing the answers to parts (f) and (g)? 35.0 Figure P7.45

k A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by = 10t² + 1tj where is in meters per second and t is in seconds. (Use the following as necessary: t.) V (a) Find its position as a function of time. ŕ= esc 10/³1 + ²/2 2²; 3 (b) Describe its motion qualitatively. The particle starts from rest at the origin, starts moving in the y direction, and gains speed faster and faster while turning to move more and more nearly parallel to the x axis. Score: 0.06 out of 0.06 Comment: (c) Find its acceleration as a function of time. a = 20ti + lj m/s² (d) Find the net force exerted on the particle as a function of time. F= T= (e) Find the net torque about the origin exerted on the particle as a function of time. N m X X (f) Find the angular momentum of the particle as a function of time. Ľ Need Help? Read It F1 N x (g) Find the kinetic energy of the particle as a function of time. K= x kg m²/s X (h) Find the power injected into the particle as a…

A skier starts at rest atop a ski slope that has a slope of exactly 37.0∘.37.0∘. Her total mass is 73.0 kg.73.0 kg. Approximating the slope to be frictionless and assuming that the skier skis straight down the slope, what will her speed ?v be after 8.00 s?

If you have a ball with a mass of 6.00kg, that has an initial velocity of vA=(2.00i + 5.00j)m/s and a final velocity of vB=(-2.00i + 8.00j)m/s, What is the change in velocity in unit vector format?   a. -4.00i + 3.00j   b. -2.83i + 3.61j   c. 4.00i – 3.00j   d. 0.00i + 13.0j

2.2. Two objects, A and B are treated as a single system. The table to the right shows some of the properties of each object at time t = 0.0 s. Use the information in the table to calculate А B color green orange 120 kg 85 kg mass -35 m the following at time t = 0.0 s: position 25 m (a) the total mass of the system (b) the total kinetic energy of the system (c) the total momentum of the system -15 m/s velocity 15 m/s temperature 15°C 25 °C (d) the position and the velocity of the cen- ter of mass of the system

vo t = 0 t = 3.5 s vo = (2.5i + 3.5j) m/s i = (-2.51) m/s The velocity of a 3.0-kg object is shown at two times. What was the magnitude of the average force exerted on the object between t= 0 and t = 3.5s? O 1.74 N O 6.26 N O 14.7 N O 3.23 N O 0.845 N

44. A 15 kg child slides, from rest, down a play- ground slide that is 4.0 m long, as shown in the figure. The slide makes a 40° angle with the horizontal. The child's speed at the bot- tom is 3.2 m/s. What was the force of friction that the slide was exerting on the child? 傳 4.0 m 40°

Michael fell asleep while driving home from school. His 1255 kg car hit a guardrail while moving at 15.98 m/s. The guardrail exerted a 6.110E4 N force on the car for 0.1233 s. After the car hit the guardrail, how fast was it moving?