Question

explain what the equivalence ( mathrm{f} cdot delta mathrm{t}=mathrm{f} cdot delta mathrm{t} ) represents. (\impulse\ alone is not an acceptable answer.)
complete the table below using the equation ( mathrm{f} cdot mathrm{t}= ) impulse. for each row, fill in the missing quantity.

	force (f)	time interval (t)	impulse (i)
b.	( 140 mathrm{~n} )	( 5 mathrm{~s} )	( 700 mathrm{~n} cdot mathrm{s} )
c.	( 400 mathrm{~n} )	( 6.0 mathrm{~s} )	( 2400 mathrm{~n} cdot mathrm{s} )
d.	( 0.17 mathrm{~n} )	( 4.5 mathrm{~s} )
e.		( 15 mathrm{~s} )	( 3,750 mathrm{~n} cdot mathrm{s} )
f.	( 1,250 mathrm{~n} )		( 3,750 mathrm{~n} cdot mathrm{s} )

Explanation:

Step1: Calculate impulse for row a

Using the formula \(I = F\times t\), substitute \(F = 80\space N\) and \(t=0.25\space s\).
\(I=80\times0.25 = 20\space N\cdot s\)

Step2: Calculate time for row b

Using the formula \(t=\frac{I}{F}\), substitute \(I = 700\space N\cdot s\) and \(F = 140\space N\).
\(t=\frac{700}{140}=5\space s\)

Step3: Calculate force for row c

Using the formula \(F=\frac{I}{t}\), substitute \(I = 2400\space N\cdot s\) and \(t = 6.0\space s\).
\(F=\frac{2400}{6}=400\space N\)

Step4: Calculate impulse for row d

Using the formula \(I = F\times t\), substitute \(F = 0.17\space N\) and \(t = 4.5\space s\).
\(I=0.17\times4.5=0.765\space N\cdot s\)

Step5: Calculate force for row e

Using the formula \(F=\frac{I}{t}\), substitute \(I = 3750\space N\cdot s\) and \(t = 15\space s\).
\(F=\frac{3750}{15}=250\space N\)

Step6: Calculate time for row f

Using the formula \(t=\frac{I}{F}\), substitute \(I = 3750\space N\cdot s\) and \(F = 1250\space N\).
\(t=\frac{3750}{1250}=3\space s\)

Answer:

a. \(20\space N\cdot s\)
b. \(5\space s\)
c. \(400\space N\)
d. \(0.765\space N\cdot s\)
e. \(250\space N\)
f. \(3\space s\)