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
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
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)*(2.60 s)+ 0.5*(-9.8 m/s2)*(2.60 s)2
d = -33.1 m (- indicates direction)
vf = vi + a*t
vf = 0 + (-9.8 m/s2)*(2.60 s)
vf = -25.5 m/s (- indicates direction)
Return to Problem 3
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
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
Given:
vi = 0 m/s
vf = 444 m/s
t = 1.83 s
Find:
a = ??
d = ??
a = (Delta v)/t
a = (444 m/s - 0 m/s)/(1.83 s)
a = 243 m/s2
d = vi*t + 0.5*a*t2
d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s2)*(1.83 s)2
d = 0 m + 406 m
d = 406 m
(Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d)
Return to Problem 6
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
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
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
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
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
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
Given:
a = -9.8 m/s2
vf = 0 m/s
t = 3.13 s
Find:
d = ??
(NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.)
First use: vf = vi + a*t
0 m/s = vi + (-9.8 m/s2)*(3.13 s)
0 m/s = vi - 30.7 m/s
vi = 30.7 m/s (30.674 m/s)
Now use: vf2 = vi2 + 2*a*d
(0 m/s)2 = (30.7 m/s)2 + 2*(-9.8 m/s2)*(d)
0 m2/s2 = (940 m2/s2) + (-19.6 m/s2)*d
-940 m2/s2 = (-19.6 m/s2)*d
(-940 m2/s2)/(-19.6 m/s2) = d
d = 48.0 m
Return to Problem 13
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
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
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
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
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
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
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
give me a short sentence of what you learned from this