1. The correct mathematical models for the first four seconds of the motion map

Question

1. The correct mathematical models for the first four seconds of the motion map below are: ( can have multiple answers)

http://tinypic.com/view.php?pic=20u4v4o&s=8#.U62fWF6aL1o << graph that goes to the question

A) x(m)=1/2(-10m/s^2)t^2(s^2)+(10m/s)t(s), 0 < t <3s

B) v(m/s)=(-10m/s^2)t(s)+(20m/s), 0 < t <3s

C) x(m)=(-10m/s) delta t(s) +5m ,3 < t <4s

D) v^2(m^2/s^2) = 2(-10m/s^2) delta x(m) +(400m^2/s^2), 0 < t <3s

2. Examine the velocity versus time graph below. Select the mathematical models that COULD describe the graph from the choices below. COULD is the operative word - is there any information about the starting point in the velocity versus time graph? (could have muliple answers)

http://tinypic.com/view.php?pic=2j3jipi&s=8#.U62g3F6aL1o <<imagae of graph

A) x(m)=1/2(+4m/s/s)t^2(s^2)-(10m/s)t(s)+5m

B) v(m/s)=(+4m/s/s)t(s)+(-10m/s)

C) delta x(m)=1/2(v(m/s)-10m/s)t(s)

D) v^2(m/s)^2=2(4m/s/s) delta x(m)+100(m/s)^2

3. A mountain goat starts a rock-slide and the rocks crash down the slope 196 m. Down hill is the positive x direction. If the rocks reach the bottom in 3 s, what is the acceleration of the rock-slide? Please remember to include units but do NOT use "^" for "raise to the power". Use ratios only.

4.NBA player Michael Jordan had one of the longest hang times in the league, about 0.92s. In general if a person has a hang time of 0.93 how high do they jump? Please use 9.81m/s/s to solve this problem.

Explanation / Answer

1 ) only C) x(m)=(-10m/s) delta t(s) +5m ,3 < t <4s
2)   B) v(m/s)=(+4m/s/s)t(s)+(-10m/s)    and    D) v^2(m/s)^2=2(4m/s/s) delta x(m)+100(m/s)^2
3) s = ut + 1/2 a*t2    ---------------> 196 = 0+ 1/2 * a * 9 =>   a = 196*2/9
                                                                                               a = 43.55 m/s2

4) v = u+at --------------> v=0 ------------> u = -at => u= 9.81*0.93 =9.114 m/s
v2 = u2+2ah   => h = -u2/2a = 9.1142 /2*9.81 = 4.23m

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