Solutions to Above Problems

1.

Given:

  a = +3.2 m/s2


  t = 32.8 s


  vi = 0 m/s


  Find:
  d = ??
  d = vi*t + 0.5*a*t2

  d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2

  d = 1720 m

  Return to Problem 1

2.

Given:

  d = 110 m


  t = 5.21 s


  vi = 0 m/s


  Find:
  a = ??
  d = vi*t + 0.5*a*t2

  110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2

  110 m = (13.57 s2)*a

  a = (110 m)/(13.57 s2)

  a = 8.10 m/ s2

  Return to Problem 2

3.

Given:

  a = -9.8 m


  t = 2.6 s


  vi = 0 m/s


  Find:
  d = ??

  vf = ??
  d = vi*t + 0.5*a*t2

  d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s2)*(2.6 s)2

  d = -33 m (- indicates direction)

  vf = vi + a*t

  vf = 0 + (-9.8 m/s2)*(2.6 s)

  vf = -25.5 m/s (- indicates direction)

  Return to Problem 3

4.

Given:

  vi = 18.5 m/s


  vf = 46.1 m/s


  t = 2.47 s


  Find:
  d = ??

  a = ??
  a = (Delta v)/t

  a = (46.1 m/s - 18.5 m/s)/(2.47 s)

  a = 11.2 m/s2

  d = vi*t + 0.5*a*t2

  d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s2)*(2.47 s)2

  d = 45.7 m + 34.1 m

  d = 79.8 m

  (Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d)

  Return to Problem 4

5.

Given:

  vi = 0 m/s


  d = -1.40 m


  a = -1.67 m/s2


  Find:
  t = ??
  d = vi*t + 0.5*a*t2

  -1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s2)*(t)2

  -1.40 m = 0+ (-0.835 m/s2)*(t)2

  (-1.40 m)/(-0.835 m/s2) = t2

  1.68 s2 = t2

  t = 1.29 s

  Return to Problem 5

6.

Given:

  vi = 0 m/s


  vf = 44 m/s


  t = 1.80 s


  Find:
  a = ??

  d = ??
  a = (Delta v)/t

  a = (444 m/s - 0 m/s)/(1.80 s)

  a = 247 m/s2

  d = vi*t + 0.5*a*t2

  d = (0 m/s)*(1.80 s)+ 0.5*(247 m/s2)*(1.80 s)2

  d = 0 m + 400 m

  d = 400 m

  (Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d)

  Return to Problem 6

7.

Given:

  vi = 0 m/s


  vf = 7.10 m/s


  d = 35.4 m


  Find:
  a = ??
  vf2 = vi2 + 2*a*d

  (7.10 m/s)2 = (0 m/s)2 + 2*(a)*(35.4 m)

  50.4 m2/s2 = (0 m/s)2 + (70.8 m)*a

  (50.4 m2/s2)/(70.8 m) = a

  a = 0.712 m/s2

  Return to Problem 7

8.

Given:

  vi = 0 m/s


  vf = 65 m/s


  a = 3 m/s2


  Find:
  d = ??
  vf2 = vi2 + 2*a*d

  (65 m/s)2 = (0 m/s)2 + 2*(3 m/s2)*d

  4225 m2/s2 = (0 m/s)2 + (6 m/s2)*d

  (4225 m2/s2)/(6 m/s2) = d

  d = 704 m

  Return to Problem 8

9.

Given:

  vi = 22.4 m/s


  vf = 0 m/s


  t = 2.55 s


  Find:
  d = ??
  d = (vi + vf)/2 *t

  d = (22.4 m/s + 0 m/s)/2 *2.55 s

  d = (11.2 m/s)*2.55 s

  d = 28.6 m

  Return to Problem 9

10.

Given:

  a = -9.8 m/s2


  vf = 0 m/s


  d = 2.62 m


  Find:
  vi = ??
  vf2 = vi2 + 2*a*d

  (0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(2.62 m)

  0 m2/s2 = vi2 - 51.35 m2/s2

  51.35 m2/s2 = vi2

  vi = 7.17 m/s

  Return to Problem 10

11.

Given:

  a = -9.8 m/s2


  vf = 0 m/s


  d = 1.29 m


  Find:
  vi = ??

  t = ??
  vf2 = vi2 + 2*a*d

  (0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(1.29 m)

  0 m2/s2 = vi2 - 25.28 m2/s2

  25.28 m2/s2 = vi2

  vi = 5.03 m/s

  To find hang time, find the time to the peak and then double it.

  vf = vi + a*t

  0 m/s = 5.03 m/s + (-9.8 m/s2)*tup

  -5.03 m/s = (-9.8 m/s2)*tup

  (-5.03 m/s)/(-9.8 m/s2) = tup

  tup = 0.513 s

  hang time = 1.03 s

  Return to Problem 11

12.

Given:

  vi = 0 m/s


  vf = 521 m/s


  d = 0.840 m


  Find:
  a = ??
  vf2 = vi2 + 2*a*d

  (521 m/s)2 = (0 m/s)2 + 2*(a)*(0.840 m)

  271441 m2/s2 = (0 m/s)2 + (1.68 m)*a

  (271441 m2/s2)/(1.68 m) = a

  a = 1.62*105 m /s2

  Return to Problem 12

13.

Given:

  a = -9.8 m/s2


  vf = 0 m/s


  t = 3.13 s


  Find:
  d = ??
     1.
        (NOTE: the time required to move to the peak of the trajectory is one-half the total hang time.)
  First use: vf = vi + a*t

  0 m/s = vi + (-9.8 m/s2)*(3.13 s)

  0 m/s = vi - 30.6 m/s

  vi = 30.6 m/s

  Now use: vf2 = vi2 + 2*a*d

  (0 m/s)2 = (30.6 m/s)2 + 2*(-9.8 m/s2)*(d)

  0 m2/s2 = (938 m/s) + (-19.6 m/s2)*d

  -938 m/s = (-19.6 m/s2)*d

  (-938 m/s)/(-19.6 m/s2) = d

  d = 47.9 m

  Return to Problem 13

14.

Given:

  vi = 0 m/s


  d = -370 m


  a = -9.8 m/s2


  Find:
  t = ??
  d = vi*t + 0.5*a*t2

  -370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s2)*(t)2

  -370 m = 0+ (-4.9 m/s2)*(t)2

  (-370 m)/(-4.9 m/s2) = t2

  75.5 s2 = t2

  t = 8.69 s

  Return to Problem 14

15.

Given:

  vi = 367 m/s


  vf = 0 m/s


  d = 0.0621 m


  Find:
  a = ??
  vf2 = vi2 + 2*a*d

  (0 m/s)2 = (367 m/s)2 + 2*(a)*(0.0621 m)

  0 m2/s2 = (134689 m2/s2) + (0.1242 m)*a

  -134689 m2/s2 = (0.1242 m)*a

  (-134689 m2/s2)/(0.1242 m) = a

  a = -1.08*106 m /s2

  (The - sign indicates that the bullet slowed down.)

  Return to Problem 15

16.

Given:

  a = -9.8 m/s2


  t = 3.41 s


  vi = 0 m/s


  Find:
  d = ??
  d = vi*t + 0.5*a*t2

  d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s2)*(3.41 s)2

  d = 0 m+ 0.5*(-9.8 m/s2)*(11.63 s2)

  d = -57.0 m

  (NOTE: the - sign indicates direction)

  Return to Problem 16

17.

Given:

  a = -3.90 m/s2


  vf = 0 m/s


  d = 290 m


  Find:
  vi = ??
  vf2 = vi2 + 2*a*d

  (0 m/s)2 = vi2 + 2*(-3.90 m/s2)*(290 m)

  0 m2/s2 = vi2 - 2262 m2/s2

  2262 m2/s2 = vi2

  vi = 47.6 m /s

  Return to Problem 17

18.

Given:

  vi = 0 m/s


  vf = 88.3 m/s


  d = 1365 m


  Find:
  a = ??

  t = ??
  vf2 = vi2 + 2*a*d

  (88.3 m/s)2 = (0 m/s)2 + 2*(a)*(1365 m)

  7797 m2/s2 = (0 m2/s2) + (2730 m)*a

  7797 m2/s2 = (2730 m)*a

  (7797 m2/s2)/(2730 m) = a

  a = 2.86 m/s2

  vf = vi + a*t

  88.3 m/s = 0 m/s + (2.86 m/s2)*t

  (88.3 m/s)/(2.86 m/s2) = t

  t = 30. 8 s

  Return to Problem 18

19.

Given:

  vi = 0 m/s


  vf = 112 m/s


  d = 398 m


  Find:
  a = ??
  vf2 = vi2 + 2*a*d

  (112 m/s)2 = (0 m/s)2 + 2*(a)*(398 m)

  12544 m2/s2 = 0 m2/s2 + (796 m)*a

  12544 m2/s2 = (796 m)*a

  (12544 m2/s2)/(796 m) = a

  a = 15.8 m/s2

  Return to Problem 19

20.

Given:

  a = -9.8 m/s2


  vf = 0 m/s


  d = 91.5 m


  Find:
  vi = ??

  t = ??
  First, find speed in units of m/s:

  vf2 = vi2 + 2*a*d

  (0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(91.5 m)

  0 m2/s2 = vi2 - 1793 m2/s2

  1793 m2/s2 = vi2

  vi = 42.3 m/s

  Now convert from m/s to mi/hr:

  vi = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

  vi = 94.4 mi/hr