1. A body moves in a straight line with a velocity whose square decreases linearly with the displacement between two points A and B, which are 300 ft apart as shown. Find the displacement of the body during the last 2 seconds before arrival at B.

2. The 14-in. spring is compressed to an 8-in. length, where it is released from rest and accelerates the sliding block A. The acceleration has an initial value of 400 ft/sec2 and then decreases linearly with the x-movement of the block, reaching 0 when the spring regains its original 14-in. length. Find the time for the block to go (a) 3 in. and (b) 6 in.

3. A car starts from rest and accelerates at a constant rate till it reaches 60 mi/hr in a distance of 200 ft, when the clutch is disengaged. The car then slows down to 30 mi/hr in an additional distance of 400 ft

with a deceleration which is proportional to its velocity. Find the time for the car to travel the 600 ft.

-----------------------------------------------

4. The x- and y-motions of guides A and B with right-angle slots control the curvilinear motion of the connecting pin P, which slides in both slots. For a short interval, the motions are governed by x = 20 + t2/4 and y = 15 - t3/6, where x and y are in mm and t is in seconds. Find the magnitudes of the velocity and acceleration of the pin for t = 2 s.

5. A projectile is launched with an initial speed of 200 m/s at an angle of 60 with respect to the horizontal. Compute the range R as measured up the incline.

6. A projectile is launched from point A with an initial speed v0 = 100 ft/sec. Determine the minimum value of the launch angle for which the projectile will land at point B.

------------------------------------------------

7. In the design of a timing mechanism, the motion of the pin A in the fixed circular slot is controlled by the guide B, which is being elevated by its lead screw with a constant upward velocity v0 = 2 m/s for an interval of its motion. Calculate both the normal and tangential components of acceleration of pin A as it passes the position for which = 30.

8. A rocket traveling above the atmosphere at an altitude of 500 km would have a free-fall acceleration g = 8.43 m/s2 in the absence of forces other

than gravitational attraction. Because of thrust, however, the rocket has an additional acceleration component a1 of 8.80 m/s2 tangent to its trajectory, which makes an angle of 30 with the vertical at the instant considered. If the velocity v of the rocket is 30 000 km/h at this position, compute the radius of curvature of the trajectory and the rate at which v is changing with time.

9. During a short interval the slotted guides are designed to move according to x = 16 - 12t + 4t2 and y = 2 + 15t - 3t2, where x and y are in millimeters and t is in seconds. At the instant when t = 2s, determine the radius of curvature of the path of the constrained pin P.

------------------------------------------------

10. The motion of the sliding block P in the rotating radial slot is controlled by the power screw. For the instant represented, measurements show

Also, the screw turns at a constant speed giving For this instant, determine the magnitudes of the velocity v and acceleration a of P.

11. The rocket is fired vertically and tracked by the radar station shown. When reaches 60, other correspond- ding measurements give the values r = 30,000 ft, Calculate the magnitudes of the velocity and acceleration of the rocket at this position.

------------------------------------------------

12. The sliders A and B are connected by a light rigid bar of length 0.5 m and move with negligible friction in the horizontal slots shown. For the position where xA = 0.4 m, the velocity of A is 0.9 m/s to the right. Determine the acceleration of each slider and the force in the bar at this instant.

13. A pilot flies an airplane at a constant speed of 600 km/h in the vertical circle of radius 1000 m. Calculate the force exerted by the seat on the 90-kg pilot at point A and at point B.

14. The cars of an amusement park ride have a speed vA = 22 m/s at A and a speed vB = 12 m/s at B. If a 75-kg rider sits on a spring scale (which registers the normal force exerted on it), determine the scale readings as the car passes points A and B. Assume that the person's arms and legs do not support appreciable force.

15. The 3-kg slider A fits loosely in the smooth 45 slot in the disk, which rotates in a horizontal plane about its center O. If A is held in position by a cord secured to point B, determine the tension in the cord for a constant rotational velocity = 300 rev/min. Would the direction of the velocity make any difference?

16. The 3000-lb car is traveling at 60 mi/hr on the straight portion of the road, and then its speed is reduced uniformly from A to C, at which point it comes to rest. Compute the magnitude F of the total friction force exerted by the road on the car (a) just before it passes point B, (b) just after it passes point B, and (c) just before it stops at point C.

17. Determine the vertical rise h of the load W during 10 seconds if the hoisting drum draws in cable at the constant rate of 180 mm/s.