2. A mass moves along a straight line, which we will call the x-axis with the po
ID: 1583382 • Letter: 2
Question
2. A mass moves along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 40.00cm + 16.00 en/s t-10.00cm/s2 t2 A. Find the object's initial velocity, initial position, and initial acceleration. B. At what time t is the velocity of the object zero? C. How long after starting does it take the object to return to its starting point? D. At what times t is the object a distance of 8.0 cm from its starting point? What is the velocity (magnitude and direction) of the mass at each of those times?Explanation / Answer
A) intial velocity = d/dt(x(t))= 16- 2*10t
put t=0, initial velocity= 16cm/s
intial distance (put t=0 in given equation) =40 + 16*0 - 10*02 = 40 cm
initial accelaration = d/dt(initial velocity) = d/dt(16- 2*10t) = -20 m/s2
B) differentiate given equation to find velocity at a certain time
d/dt(x(t))= 16 - 2*10*t
put d/dt(x(t))= 0 that is
16- 2*10*t =0
t = 16/20 = 0.8 sec
C) put x(t)=40 in above equation,
40 = 40 +16*t -10*t2
solving for t we get
16*t = 10*t2
hence t= 0sec and t= 1.6 sec
so it will return at its original place at t= 1.6sec
D) put x(t) =8 in above equation and solve for t that is
8 = 40 +16*t -10*t2
t = 2.75 sec
for velocity differentiate x(t) that is we get
velocity = 16 - 2*10t
put t= 2.75 sec
velocity = 16- 2*10*2.75 = -39 cm/s
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