Assignment-1 engineering dynamics last date 20-02-2014

1.A ball is thrown vertically upward with a speed of 15 m/s.Determine the time of flight when it returns to its original position?

Fig.1 fig.22.A particle travels along a straight line with a velocity of v = (20 - 0.05s2) mis,where s is in meters. Determine the acceleration of the particle at s = 15 m.

3.A particle travels along a straight line with a velocity v = (12 – 3t2) m/s, where t is in seconds. When t = 1 s, the particle is located 10 m to the left of the origin. Determine the acceleration when t = 4 s, the displacement from t = 0 to t = 10 s, and the distance the particle travels during this time period.

4. A car has an initial speed of 25 m/s and a constant deceleration of 3 m/s2. Determine the velocity of the car when t = 4 S. What is the displacement of the car during the 4-s time interval? How much time is needed to stop the car?

5.The particle travels along a straight track such that its position is described by thes-t graph. Construct the v-t graph for the same time interval.

Fig.5 fig.6

6.A van travels along a straight road with a velocity described by the graph.Construct the s-t and a-t graphs during the same period. Take s = 0 when t = O.

7.The dragster starts from rest and has a velocity described by the graph. Constructthe s-t graph during the time interval O ≤ t ≤ 15 s. Also, determine the total distancetraveled during this time interval.

Fig.7 fig.88.The dragster starts from rest and has an acceleration described by the graph.Construct the v-t graph for the time interval 0 ≤ t ≤t' , where t' is the timefor the car to come to rest.

9.A train starts from station A and for the first kilo-meter, it travels with a uniformacceleration. Then, for the next two kilometers, it travels with a uniform speed.Finally, the train decelerates uniformly for another kilometer before coming to rest atstation B. If the time for the whole journey is six minutes, draw the v-t graph anddetermine the maximum speed of the train.

10.A two-stage missile is fired vertically from rest with the acceleration shown. In15 s the first stage A burns out and the second stage B ignites. Plot the v-t and s-tgraphs which describe the two-stage motion of the missile for o ≤ t ≤20 s.

Fig.10 fig.1211.A particle travels along a curve defined by the equation s = (t3 - 3t2 + 2t) m. where t is in seconds. Draw the s - t, v - t, and a - t graphs for the particle foro ≤ t ≤ 3 s.

12.The snowmobile moves along a straight course according to the v-t graph.Construct the s-t and a-t graphs for the same 50-s time interval. When t = 0, s = O.

13.A missile starting from rest travels along a straight track and for 10 s has anacceleration as shown. Draw the v-t graph that describes the motion and find thedistance traveled in 10 s.

Fig.13 fig,14

14.The rocket has a n acceleration described by the graph. If it starts from rest,construct the v-t and s-t graphs for the motion for the time interval 0 ≤S ≤ 1 4 s .

15.If the x and y components of a particle's velocity are Vx = (32t) m/s and Vy = 8m/s, determine the equation of the path y = f(x). x = 0 and y = 0 when t = O.

16.A particle is traveling along the parabolic path y = 0.25x2• If x = (2t2) m, where tis in seconds, determine the magnitude of the particle's velocity and accelerationwhen t = 2 s. The ball is kicked from point A with the initial velocity v A = 10 m/s. Determine the range R, and the speed when the ball strikes the ground.

Fig.16 Fig.21

17.The velocity of a particle is v = {3i + (6 - 2t)j } mis, where t is in seconds. If r =0 when t = 0, determine the displacement of the particle during the time intervalt = 1 s to t = 3 s.

18.A particle travels along the parabolic path y = bx2. If its component of velocityalong the y axis is Vy = et2, determine the x and y components of the particle'sacceleration. Here b and e are constants.

19. The velocity of a particle is given by v = { 16t2i + 4t3j + (5t + 2)k} mis, wheret is in seconds. If the particle is at the origin when t = 0, determine the magnitude ofthe particle's acceleration when t = 2 s. Also, what is the x, y, Z coordinate positionof the particle at thisinstant?

20. A particle travels along the circular path X2 + Y2 = r2. If the y component of theparticle's velocity Vy = 2r cos2t, determine the x and y components of itsacceleration at any instant.

21.The van travels over the hill described by y = ( - 1 .5(10-3) x2 + 15) ft. If it has aconstant speed of 75 ft/s, determine the x and y components of the van'svelocity and acceleration when x = 5 0 ft.

22.The ball is thrown off the top o f the building. If it strikes the ground at B in 3 s,determine the initial velocity vA and the inclination angle A at which it was thrown.ɵ

Also, find the magnitude of the ball's velocity when it strikes theground.

Fig.22 fig.23

23.The baseball player A hits the baseball with VA = 40 ft/s and ɵA= 60°. When

the ball is directly above of player B he begins to run under it. Determine theconstant speed VB and the distance d at which B must run in order to make thecatch at the same elevation at which the ball was hit.

24.The golf ball is hit a t A with a speed o f VA = 40 m/s and directed at an angle of30° with the horizontal as shown. Determine the distance d where the ball strikes theslope at B.

Fig.24 fig.25

25.The boat is traveling along the circular path with a speed of v = (0.0625t2) m/s,where t is in seconds. Determine the magnitude of its acceleration when t = 10 s.

26.If the motorcycle has a deceleration of at = - (0.00ls) m/s2 and its speed atposition A is 25 m/s, determine the magnitude of its acceleration when it passespoint B.

Fig.26 Fig.27

27.The car is traveling along the road with a speed of v = (300/s) m/s, where s is inmeters. Determine the magnitude of its acceleration when t = 3 s if t = 0 at s = O.

28.An automobile is traveling on a horizontal circular curve having a radius of 800ft. If the acceleration of the automobile is 5 ft/S2, determine the constant speed atwhich the automobile is traveling.

29. A car travels along a horizontal circular curved road that has a radius of 600 m.If the speed is uniformly increased at a rate of 2000 km/h2, determine the magnitudeof the acceleration at the instant the speed of the car is60 km/h.

30. The automobile has a speed of 80 ft/s at point A and an acceleration a having amagnitude of 1 0 ft/S2, acting in the direction shown. Determine the radius ofcurvature of the path at point A and the tangential component of acceleration.