- #1
agargento
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- 2
Homework Statement
The motion of a particle moving in a circle in the x-y plane is described by the equations: r(t)=3.15, Θ(t)=8.86t
Where Θ is the polar angle measured counter-clockwise from the + x-axis in radians, and r is the distance from the origin in m.
1. Calculate the x-coordinate of the particle at the time 2.20 s.
2. Calculate the y-component of the velocity at the time 2.20 s?
3. Calculate the magnitude of the acceleration of the particle at the time 1.60 s?
4. By how much does the speed of the particle change from t=10 s to t=51 s?
5. Calculate the x-component of the acceleration at the time 2.60s?
Homework Equations
x(t) = Rcos(ωt)
y(t) = Rsin(ωt)
And their derivatives for velocity and acceleration.
The Attempt at a Solution
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I got every question except for 4.
1. 2.52 m
2. 22.34 m/s
3. 247 m/s^2
4.
5. 124.13 m/s^2
For 4 I tried a couple of things. The first was to multiply 247*41 but that didn't work. The next thing I did was to use the equation for velocity (The derivatives of the equations above) to find the X and Y component of the velocity of each time (x,y when t=51 and x,y t=10), calculate their magnitude, and then subtract them from each other, didn't work either.
What am I missing?