Please solve the following questions! Find the x component of the acceleration a

Question

Please solve the following questions!

Find the x component of the acceleration at the final time.

Find the magnitude of the acceleration at the final time.

Find the x-component of the average velocity of the asteroid.

Find the y-component of the average velocity of the asteroid.

Find the speed of the asteroid at the final time.

Find the magnitude of the average acceleration of the asteroid.

Thank you!

The velocity as a function of time for an asteroid in the asteroid belt is given by vnt ve where Vo and to are constants Use ti 0 as the initial time, and t, -1.9t as the final time The values for the constants that you will use are: vo 14 m/s to 347 s

Explanation / Answer

Here v(t) = v0e-t/t0 i + v0t/2t0 j

The x-component of velocity is vx(t) = v0e-t/t0 (the i component of the vector) and

y-component of velocity is vy(t) = v0t/2t0

The time derivative of a vector v is acceleration

ax = dvx(t)/dt = -v0/t0*e^-t/t0 evaluated at t = final time

If a is the acceleration vector, that is a = ax*i + ay*j

ax = -v0/t0*e-t/t0 = 6.03*10-3 m/s2
ay = dvy(t)/dt = v0/2t0 = 14/2*347 = 2.017*10-2 m/s2

Average Acceleration = 0.02105 m/s2

The position vector r(t) is v(t)dt = -v0*t0*e^-(t/t0)*i + [v0*t²/2]*j + C

r(0) = 0 at t = 0 then -v0*t0*i = C and C = v0*t0*i

r(t) = v0*t0*[1 - e^=(t/t0)]*i + [v0*t²/2]*j

r = r(tf) - r(ti)

aavg = [v(tg) - v(ti)]/(tf - ti) (final velocity minus initial velocity divided by the time)

vavg =[s(tf) - s(ti)]/(tf - ti) (final position minus initial position divided by the time)

speed = |v| = [vx² + vy²]

vx = v0*e^(-t/t0) = 2.0939 m/s and vy = [v0*t/(2t0)] = 13.3 m/s

average speed = ((13.3)2 + (2.0939)2)1/2 = 13.46 m/s

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