Problem Solving Equations
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Equations and Problem-Solving * An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off. -------------------------------------------------
Solutions
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
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Equations and Problem-Solving * A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. -------------------------------------------------
Solutions
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
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Equations and Problem-Solving
* Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels?
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Solutions
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)
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Equations and Problem-Solving
* A kangaroo is capable of jumping to a height of 2.62 m. Determine the take-off speed of the kangaroo.
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Solutions
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 =
Equations and Problem-Solving * An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off. -------------------------------------------------
Solutions
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
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Equations and Problem-Solving * A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. -------------------------------------------------
Solutions
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
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Equations and Problem-Solving
* Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels?
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Solutions
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)
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Equations and Problem-Solving
* A kangaroo is capable of jumping to a height of 2.62 m. Determine the take-off speed of the kangaroo.
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Solutions
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 =