school
Acemy

Straight-Line Motion: Position, Velocity, Acceleration

AP Calculus AB· difficulty 3/5

A particle with s(t)=t3−6t2+9ts(t) = t^3 - 6t^2 + 9t is <strong>speeding up</strong> when

  • A

    1<t<21 < t < 2 and t>3t > 3

    check_circle
  • B

    0<t<10 < t < 1 and 2<t<32 < t < 3

  • C

    t>3t > 3 only

  • D

    0<t<10 < t < 1 only

Explanation

Speeding up means vv and aa have the same sign. v(t)=3(t−1)(t−3)v(t) = 3(t-1)(t-3): positive on t<1t<1 and t>3t>3, negative on 1<t<31<t<3. a(t)=6(t−2)a(t) = 6(t-2): negative for t<2t<2, positive for t>2t>2. Same-sign intervals: 1<t<21<t<2 (both negative) and t>3t>3 (both positive).

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode