Find the velocity vector for a particle whose position vector is vector components 2t, 5 for all t. (10 points)
A) vector components 2, 0
B) vector components t squared, 5 times t
C) vector components t cubed over 3, 5 times t squared over 2
D) the square root of the quantity 4 times t squared plus 25
r = <2t,5>
r' = <2,0>
To find the velocity vector for a particle, we need to differentiate the position vector with respect to time.
Given that the position vector is (2t)i + 5j, we will differentiate each component separately to find the velocity vector.
Differentiating the first component, 2t, with respect to time (t), we get d(2t)/dt = 2.
Differentiating the second component, 5, with respect to time (t), we get d(5)/dt = 0.
Therefore, the velocity vector is (2i + 0j).
From the options given:
A) vector components 2, 0: This matches the calculated velocity vector.
B) vector components t squared, 5 times t: This doesn't match the calculated velocity vector.
C) vector components t cubed over 3, 5 times t squared over 2: This doesn't match the calculated velocity vector.
D) the square root of the quantity 4 times t squared plus 25: This is not even a vector.
Hence, the answer is A) vector components 2, 0.