Unit 1 Review

Mathematical introduction to physics

1.     Express  a:     v=  square root of  2as

v² = 2as à v²/2s = a

2.     Express t:      v =  v₀  +  at

(v-v₀)/a = t

3.     Express  c:      E  =  mc²

E/m = c² à sqrt(E/m) = c

Solve the following (include units)         N = Kgm/s²    j = Nm   W=j/s

                                   

4.     2.5x10¹² m/s²  x   3.3x10¹³ s  = (8.25x10²⁵)m/s

5.     3.5x10^-4kg  x  2.5x10^-10m/s² = (8.75x10^-14)N

6.     6.5x10⁵m/s  :    3.3x10^-3s  = (1.97x10⁸)m/s²

7.     2x10⁵N    :     3x10¹⁵m/s² = (6.67x10^-11)Kg

8.     2.4x10⁶w  *  2.3x10³s  = (5.52x10⁹)j

Can these equations be correct?  Use dimensional analysis of units to prove your point!   d (m)     v (m/s)      t (s)     a (m/s2)

1.     d = v/t   à m = (m/s)/s à m = m/s² NOT VALID    

2.     d = vt + at²/2 à m = (m/s)(s) + (m/s²)(s²)/2 à m = m + m/2 VALID

3.     v = 2ad à (m/s) = 2(m/s²)(m) à (m/s) = (m²/s²) NOT VALID

                                                                                     

Solve (your answer should be stated in MKS units)

1.     5.3x10³km + 20m  = 5300000m + 20m = 5300020m                   

2.     0.5m/s + 2km/h  =  0.5m/s + 0.56m/s = 1.06m/s

3.     5.5x10³ g + 20 kg = 5.5kg + 20kg = 25.5kg                          

4.     42cm + 2m  = 0.42m + 2m = 2.42m

 

Find the angles         a                               a= 15         b= 22

                                               b

∠A = tan^-1(15/22) = 34.3⁰                                              

c = 26.6

∠B = cos^-1(15/26.6) = 55.7⁰               b                                

                                                                         25⁰       

Find the sides a and  b          a                    

           25

a à sin(25⁰) = a/25 à a = 10.6

b à cos(25⁰) = b/25 à b = 22.7

Use units and dimensional analysis to find out if the formulas are valid

1.     Distance = speed * time à m = (m/s)*s à VALID                         

2.     acceleration = speed/time à (m/s²) = (m/s)/(s) à VALID

3.     Force = mass * acceleration à N = kg*(m/s²) à VALID                    

4.     distance = energy * time à m = (j)*(s) à NOT VALID

5.     Power = work * time à (j/s) = (j)*(s) à NOT VALID                              

6.     speed = power/force à (m/s) = (j/s)/(N) à VALID

The displacement of an object from a start point was checked at 2 s intervals. The results are in the following chart

Time (t) in (s)	Displacement (d) in (m)
0	0
2	4
4	8.5
6	12.2
8	15.8
10	21
12	25.3

a.     Graph the results using proper graphing techniques.

b.     What is the relationship you observe?

c.      Find the constant (slope) including units. What quantity does it represent?

d.     Write the equation of the line.

e.      Show one example of interpolation and one for extrapolation.