A subatomic particle is moving in the y direction. Its position y at any time t

Question

A subatomic particle is moving in the y direction. Its position y at any time t is described by y(t) = 3t^3 + 10t^2 + 4. What is the particle's position when t = 2? What is the particle's velocity when t = 2? Box 1: Enter your answer as a whole or decimal number. Examples 3, -4, 5.5 Enter DNE for Does Not Exist, infinity of Infinity Box 2: Enter your answer as a whole or decimal number. Examples: 3, -4, 5.5 Enter DNE for Does Not Exist, infinity for Infinity Another subatomic particle is moving in the x direction. Its position x at any time t is described by x(t) = 3t^2 + 5t + 10. At what point in time does the particle have a velocity of 20 m/s? t =. Box 1: Enter your answer a whole or decimal number. Examples: 3, -4. 5.5 Enter DNE for Does Not Exist, infinity for Infinity.

Explanation / Answer

Given particle positoin

y(t) = 3t3 +10t2 +4

at t=2

y(2) = 3(2)3 + 10(2)2 + 4=24+40+4=68 --->>>Ans

v(t) = d/dt(y(t)) = d/dt ( 3t3 +10t2 +4)

v(t) = 9t2+20t+0

v(2)= 9(2)2 + 20(2) = 76 ----->Ans

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given x(t) = 3t2+5t+10

velocity function v(t) = d/dt (  3t2+5t+10 )

20 m/s = 6t+5

15 = 6t

t=2.5 ----->Ans

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