Here are 4 particles that move along the x-axis with their 4 different respectiv

Question

Here are 4 particles that move along the x-axis with their 4 different respective position functions:

1. x(t) = 2t^2 -4
2. x(t) = -3t -4
3. x(t) = -2t^2 -4
4. x(t) = 2(sqrt(t+1)) -4

Which ones are speeding up for 0<t<infinity?

A) only 1 B) 1,3,4 C) all D) none E) 1 and 4

Please explain answer. I thought that taking the derivative, finding its sign, then taking another derivative, and finding its sign, would show me which particles are speeding up. (Recall: when the sign between velocity and acceleration differs it is slowing down and when they are the same, one increases in speed.) But that leaves me only with 1 and 3, which isn't an answer choice.

Explanation / Answer

v = 4t = +ve    a = 4 = +ve =>speeding up v = (t+1)^-1/2 = +ve a = -2/3(t+1)^-3/2 => -ve => slowing down

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