Physics 107 homework assignment #1 Cutnell & Johnson, 7th



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28. REASONING AND SOLUTION The car enters the speedway with a speed of
v01 = a1t1 = (6.0 m/s2)(4.0 s) = 24 m/s
After an additional time, t, it will have traveled a distance of
x = v01t + a1t2/2
to overtake the other car. This second car travels the same distance x = v02t.

Equating and solving for t yields



30. REASONING The drawing shows the two knights, initially separated by the displacement d, traveling toward each other. At any moment, Sir George’s displacement is xG and that of Sir Alfred is xA. When they meet, their displacements are the same, so xG = xA.




According to Equation 2.8, Sir George's displacement as a function of time is


(1)
where we have used the fact that Sir George starts from rest

Since Sir Alfred starts from rest at x = d at t = 0 s, we can write his displacement as (again, employing Equation 2.8)


(2)
Solving Equation 1 for t2 and substituting this expression into Equation 2 yields

(3)

Noting that xA = xG when the two riders collide, we see that Equation 3 becomes




Solving this equation for xG gives .


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