Please help me to solve this step by step.

1. A particle of mass m = 2.0 kg is moving in a plane. It can be described by its position function F(t) = (4.0 t3 18 2'2 +24 t) ?+ (3.0 t4 8.0 t3 +12) }+(6.0 t2 24 t12)I; where F is in m and t 2 Dis in seconds. (a) What is the speed of this particle at t= 1.0 s? (b) Is it possible for this particle to have zero velocity? When? (c) Is this particle moving with constant acceleration? Ans m- ,a- m 2. An object is projected from the top of a building with an initial speed of 12.2 m/s and an angle of 53.00 above the horizontal. The object then hits the ground a horizontal distance of 25.0 m from the building. (a) Set up proper coordinates and ll out the following known and unknown quantities with proper signs (+ or -) on the diagram. Use proper notation if a quantity is unknown, for example, use 120 for the initial velocity. Note that in (b) to (d) you need to use the values (included + and -) listed in (a). S: H x0: y0: (v0)1= 1 x: _ y= (v0)y= a (b) How long does it take to strike the ground? (0) How tall is the building? (d) What is the speed when the object strikes the ground An S. (b)-, (c), -(d), 3. A stone is projected at a cliff of height h with an initial speed of 42.0 m/s directed at angle 6!] = 60.0 above the horizontal. The stone strikes at A, 5.50 s after launching. Find (a) the height h of the cliff, (b) the speed of the stone just before impact at A, and (c) the maximum height H reached above the ground. Ans. (a) l (b) " H m l 4. An object of mass m1 = 5.0 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2 = 9.0 kg as shown in the Figure (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects and (c) the tension in the string. (b) a = 6.30 m/s2 _ _. (c) T = 32.1 N .m 5. Block A has mass mA : 4.0 kg , and block B has mass m3 : 2.0 kg . The coefcient of kinetic 'iction between block B and the horizontal plane is ,uk = 0.5 . The inclined plane is ictionless and at angle 6' = 300 .The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Frini: no lose. in E: (a) Draw the FBD of blocks A and B. Set up "MN?\" punt" B proper coordinates. Decompose forces if it 5. Block A has mass mA = 4.0 kg , and block B has mass m = 2.0 kg . The coefficient of kinetic friction between block B and the horizontal plane is /, = 0.5 . The inclined plane is frictionless and at angle 0 = 30 .The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass Frictionless, (a) Draw the FBD of blocks A and B. Set up massless pulley proper coordinates. Decompose forces if it is necessary. (b) Find the tension in the cord? 10 (c) Find the magnitude of the acceleration of the blocks. (d) What is the force exerted on block A by the incline? "b) T =13.06 N (c) a = 1.63 m/s2 (d) FNA = 33.95 N(d) What is the force exerted on block A by the incline? (b) T =13.06 N (c) a = 1.63 m/s2 (d) FN.A = 33.95 N 6. The figure shows a block 1 of mass m, = 2.0 kg and block 2 of mass m2 = 1.0 kg are connected by a string of negligible mass. Block 2 is pushed by a force F of magnitude 20 N and angle 0 =350. The coefficient of kinetic friction between each block and the horizontal surface is 0.20. m 1 (a) Draw the FBD of each block. Set up proper coordinates. Decompose force if it is necessary. (b) What is the acceleration of the blocks? (c) What is the tension in the string? (b) a = 2.737 m/s (c) T = 9.4 N