For part b, you can use the equation for acceleration, which is the second derivative of velocity with respect to time. To find the x component of the acceleration at the final time, you can take the second derivative of the x component of the velocity equation with respect to time and then evaluate it at the final time.
For part c, you can use the equation for acceleration, which is the second derivative of velocity with respect to time. To find the magnitude of the acceleration at the final time, you can take the second derivative of the velocity equation with respect to time, then calculate the magnitude of the resulting vector and then evaluate it at the final time.
For part d, you can use the equation for average velocity, which is the change in displacement divided by the change in time. To find the x component of the average velocity of the asteroid, you can take the x component of the displacement equation and divide it by the change in time (472 s).
The velocity as a function of time for an asteroid in the asteroid belt is given by
v(t)= vo e^(-t/to)i + (vo t/ 2 to) j
with vo and to constants.
Use ti = 0 as the initial time, and tf = 472 s as the final time.
The values for the constants that you will use are:
vo = 9 m/s
to = 590 s
a) Find the displacement of the asteroid.
After integrating the x and y components I found the displacement to be:
2.92×10^3 i + 8.50 ×10^2 j
Which was correct.
But now the question asks to:
b) Find the x component of the acceleration at the final time.
c) Find the magnitude of the acceleration at the final time.
d)Find the x-component of the average velocity of the asteroid.
I want to understand how to go about solving these, I'm not looking for answers.
1 answer
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