Question

true or false: a particle is slowing down when v(t) and a(t) have the same sign. true or false: a particle’s displacement over the first a seconds is s(a) - s(0)

Explanation:

Step1: Analyze velocity - acceleration relationship

A particle is speeding up when \(v(t)\) and \(a(t)\) have the same sign and slowing down when \(v(t)\) and \(a(t)\) have opposite signs. So the statement "A particle is slowing down when \(v(t)\) and \(a(t)\) have the same sign" is False.

Step2: Recall displacement formula

The displacement of a particle over the time - interval \([0,a]\) is given by the change in its position function. If \(s(t)\) is the position function of the particle, then the displacement over the first \(a\) seconds is \(s(a)-s(0)\). So this statement is True.

Answer:

1. False
2. True