12. t- o and t n to, a rocket movns stralght upward with an acceleration given b

Question

12. t- o and t n to, a rocket movns stralght upward with an acceleration given by )-A-, where A and 8 are constants. (Assume a is in ms) (a) If x is in meters and t is in seconds, what are the units of A and B? (use the following as necessarny: m and s) units of A units of B “ (b) If the rocket starts from rest, how does the velocity vary betweenO and f "to? (Enter the rocket's velocity as a furction of time., Use the following as necessary: A, B, and t (c) If its initial position is zero, what is the rocket's position as a function of time during this same time interval? (Use the following as necessary: A, B, and t.) Submit Assignment Save Assignment Progres Home My Assignments

Explanation / Answer

given acceleration of rocket = A-Bt0.5

a)unit of A should be m/s2

unit of B = m/s1.5

b)acceleration = dv/dt=A-Bt0.5

dv = (A-Bt0.5)dt

velocity as a function of time is obtained by integrating (A-Bt0.5)dt over 0 and t

v(t) = At-Bt1.5/1.5

c) let position be denoted by s

ds/dt = v(t)

ds/dt = At-Bt1.5/1.5

ds=(At-Bt1.5/1.5)dt

the position as a function of time can be obtained by integrating (At-Bt1.5/1.5)dt over 0 and t

s(t) = (At2/2)-(Bt2.5/3.75)

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