The velocity v of a particle moving in the xy plane is given by v = (4.0t -4.0t^

Question

The velocity v of a particle moving in the xy plane is given by v = (4.0t -4.0t^2)j + 6.5j, in m/s. Here v is in m/s and t (for positive time) is in s. What is the acceleration when t = 3.0 s? j-component of acceleration? (in m/s^2) -1.57 times 10^14 -1.77 times 10^1 -2.00 times 10^1 -2.26 times 10^1 -2.55 times 10^1 -2.89 times 10^1 -3.26 times 10^1 -3.68 times 10^1 j-component of acceleration? (in m/s^2) 0.00 5.35 times 10^-1 7.76 times 10^-1 1.12 1.63 2.37 3.43 4.97 What is the centripetal acceleration of an object on the Earth's equator owing to the rotation of the Earth? (in m/s^2) 3.37 times 10^-2 4.89 times 10^-2 7.09 times 10^-2 1.03 times 10^-1 1.49 times 10^-1 2.16 times 10^-1 3.14 times 10^-1 4.55 times 10^-1 What would the period rotation from of (in hours = h) of the 1 the Earth have to be for objects on the equator to have a centripetal acceleration equal to 9.80 m/s? (in h) 5.99 times 10^-1 7.96 times 10^-1 1.06 1.41 1.87 2.49 3.31 4.41

Explanation / Answer

7 . Vx = 4t - 4t^2

a_X = d(Vx)/dt = 4 - 8t

t = 3s

a_x = 4 - 24 = -20 m/s^2

Ans(C)

8. Vy = 6.5

ay = dVy/dt = 0

Ans(A)

9. T = 24 hrs = 24 x 3600 s

w = 2pi / T

a_c = w^2 Re = (2 pi / (24 x 3600))^2 ( 6.371 x 10^6)

= 3.37 x 10^-2

Ans(A)

10. 9.80 = w^2 (6.371 x 10^6)

w = 1.24 x 10^-3 rad /s

T = 2pi / w = 5066 sec

T (in h ) = 5066 / 3600 = 1.41

Ans(D)

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