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.

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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.

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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) -------------------------------------------------
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 =...
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