Worksheet: Acceleration Vectors

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

Q1:

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 ( 2 6 5 + 2 0 . 0 ) i j m/s
  • B ( 2 6 2 + 3 0 . 0 ) i j m/s
  • C ( 2 7 3 + 2 4 . 0 ) i j m/s
  • D ( 2 7 0 + 2 3 . 0 ) i j m/s
  • E ( 2 6 7 + 2 7 . 0 ) i j m/s

Q2:

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 . 0 βˆ’ 8 . 0 ) i k m/s
  • B ( βˆ’ 1 6 . 0 + 8 . 0 ) i k m/s
  • C ( 1 6 . 0 + 8 . 0 ) i k m/s
  • D ( 8 . 0 + 6 . 0 ) i k m/s
  • E ( 6 . 0 + 6 . 0 ) i k m/s

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

  • A ( 4 . 0 + 2 . 0 ) i k m/s
  • B ( 2 . 0 + 4 . 0 ) i k m/s
  • C ( 3 . 5 + 3 . 5 ) i k m/s
  • D ( 4 . 0 + 3 . 0 ) i k m/s
  • E ( 4 . 0 + 3 . 0 ) i k m/s

Q3:

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 ) i j m/s2
  • B ( 1 . 7 βˆ’ 0 . 9 ) i j m/s2
  • C ( 2 . 9 βˆ’ 3 . 7 ) i j m/s2
  • D ( βˆ’ 3 . 7 βˆ’ 2 . 9 ) i j m/s2
  • E ( βˆ’ 1 . 7 βˆ’ 0 . 9 ) i j m/s2

Q4:

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?

  • A βˆ’ 2 . 9 i m/s
  • B 4 . 6 i m/s
  • C ( 4 . 6 βˆ’ 2 . 9 ) i k m/s
  • D ( 4 . 6 + 2 . 9 ) i j m/s
  • E βˆ’ 2 . 9 k m/s

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

  • A 4 . 6 i m/s2
  • B ( 4 . 6 βˆ’ 2 . 9 ) i k m/s2
  • C 2 . 3 i m/s2
  • D 4 . 4 j m/s2
  • E ( 0 + 0 + 0 ) i j k m/s2

Q5:

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

  • A βˆ’ 8 i m/s2
  • B βˆ’ 4 i m/s2
  • C βˆ’ 1 0 i m/s2
  • D βˆ’ 2 i m/s2
  • E βˆ’ i m/s2

Q6:

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 . 0 βˆ’ 2 0 ) i j k m/s2
  • B ( 1 5 + 1 6 βˆ’ 2 6 ) i j k m/s2
  • C ( 1 0 + 1 6 βˆ’ 1 6 ) i j k m/s2
  • D ( 5 . 0 + 4 . 0 βˆ’ 2 4 ) i j k m/s2
  • E ( 5 . 5 + 1 6 βˆ’ 1 4 ) i j k m/s2

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

Q7:

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.