Worksheet: Acceleration Vectors

In this worksheet, we will practice calculating the resultant vector of multiple linear accelerations that are at angles to each other.


A spaceship is traveling at a constant velocity vi=250/ms when its rockets fire, giving it an acceleration aij=(3.00+4.00)/ms. What is the spaceship’s velocity 5.00 s after the rockets fire?

  • A(265+20.0)ij m/s
  • B(262+30.0)ij m/s
  • C(273+24.0)ij m/s
  • D(270+23.0)ij m/s
  • E(267+27.0)ij m/s


The position of a particle is given by rijk(𝑑)=(4.0π‘‘βˆ’3.0+2.0𝑑)m.

What is the velocity of the particle at 0.0 s?

What is the velocity of the particle at 1.0 s?

  • A(8.0βˆ’8.0)ik m/s
  • B(βˆ’16.0+8.0)ik m/s
  • C(16.0+8.0)ik m/s
  • D(8.0+6.0)ik m/s
  • E(6.0+6.0)ik m/s

What is the average velocity of the particle between 0.0 s and 1.0 s?

  • A(4.0+2.0)ik m/s
  • B(2.0+4.0)ik m/s
  • C(3.5+3.5)ik m/s
  • D(4.0+3.0)ik m/s
  • E(4.0+3.0)ik m/s


A particle accelerates uniformly. At the time 𝑑=0.0 s the particle has a velocity vij=(14+22) m/s. At 𝑑=3.8 s, the particle has a velocity vij=(0.0+11) m/s. What is the acceleration of the particle?

  • A(3.7+2.9)ij m/s2
  • B(1.7βˆ’0.9)ij m/s2
  • C(2.9βˆ’3.7)ij m/s2
  • D(βˆ’3.7βˆ’2.9)ij m/s2
  • E(βˆ’1.7βˆ’0.9)ij m/s2


The displacement of a particle is given by rijk=(2.3𝑑+4.4βˆ’2.9𝑑) m.

What is the velocity of the particle at 𝑑=0?

  • Aβˆ’2.9i m/s
  • B4.6i m/s
  • C(4.6βˆ’2.9)ik m/s
  • D(4.6+2.9)ij m/s
  • Eβˆ’2.9k m/s

What is the acceleration of the particle at 𝑑=0?

  • A4.6i m/s2
  • B(4.6βˆ’2.9)ik m/s2
  • C2.3i m/s2
  • D4.4j m/s2
  • E(0+0+0)ijk m/s2


A particle has the position function rijk(𝑑)=((10π‘‘βˆ’π‘‘)+5𝑑+5𝑑) m. What is the acceleration vector of the particle?

  • Aβˆ’8i m/s2
  • Bβˆ’4i m/s2
  • Cβˆ’10i m/s2
  • Dβˆ’2i m/s2
  • Eβˆ’i m/s2


A particle has a velocity given by vijk(𝑑)=ο€Ή5.0𝑑+π‘‘βˆ’2.0𝑑/ms.

What is the particle’s acceleration vector at 𝑑=2.0s?

  • A(5.0+6.0βˆ’20)ijk m/s2
  • B(15+16βˆ’26)ijk m/s2
  • C(10+16βˆ’16)ijk m/s2
  • D(5.0+4.0βˆ’24)ijk m/s2
  • E(5.5+16βˆ’14)ijk m/s2

What is the magnitude of the particle’s acceleration at 𝑑=2.0s?


At the instant 𝑑=0s, a skier is skiing with an acceleration of 2.1 m/s2 downward along a slope angled 15∘ below the horizontal, as shown in the diagram. The skier’s initial position vector is rij=(75βˆ’50)m and his initial velocity vector is vij=(4.1βˆ’1.1)/ms.

At the instant 𝑑=10s, what is the skier’s displacement vector from the point that they occupied at 𝑑=0s?

  • A(220βˆ’88)ij m
  • B(180βˆ’80)ij m
  • C(210βˆ’90)ij m
  • D(190βˆ’98)ij m
  • E(230βˆ’82)ij m

What is the skier’s velocity vector at the instant 𝑑=10s?

  • A(26βˆ’5.4)ij m/s
  • B(24βˆ’6.5)ij m/s
  • C(26βˆ’5.6)ij m/s
  • D(25βˆ’4.5)ij m/s
  • E(22βˆ’6.6)ij m/s

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