Straight-Line Motion: Position, Velocity, Acceleration Practice

Sample questions

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1. Sample 1difficulty 2/5

   A particle has position $s(t) = t^3 - 3t^2 + 4$ (m, s). Its velocity at $t = 2$ is

   • A

     $12~\text{m/s}$

   • B

     $3~\text{m/s}$

   • C

     $0~\text{m/s}$

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   • D

     $6~\text{m/s}$

   Why

   $v(t) = s'(t) = 3t^2 - 6t$. $v(2) = 12 - 12 = 0$.

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2. Sample 2difficulty 2/5

   A particle moving in the positive direction with positive acceleration is

   • A

     Speeding up

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   • B

     Slowing down

   • C

     Cannot tell

   • D

     At rest

   Why

   Same signs of $v$ and $a$ → speeding up.

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3. Sample 3difficulty 2/5

   For $s(t) = t^3 - 6t^2$, the acceleration at $t = 1$ is

   • A

     $-12$

   • B

     $12$

   • C

     $-6$

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   • D

     $6$

   Why

   $v(t) = 3t^2 - 12t$, $a(t) = 6t - 12$. At $t = 1$: $-6$.

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4. Sample 4difficulty 2/5

   A particle's position is $s(t) = 16 - t^2$ (meters, seconds). Its velocity at $t = 3$ is

   • A

     $+6~\text{m/s}$

   • B

     $0$

   • C

     $+9~\text{m/s}$

   • D

     $-6~\text{m/s}$

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   Why

   $s'(t) = -2t$. At $t=3$: $-6~\text{m/s}$.

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5. Sample 5difficulty 2/5

   The velocity graph is a straight line. The acceleration is:

   • A

     Constant and negative

   • B

     Constant and positive

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   • C

     Increasing

   • D

     Zero

   Why

   A linear $v(t)$ with positive slope means $a(t) = v'(t)$ is constant and positive.

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