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CAIE A-Level Physics 1.4 Scalars and Vectors

Practise classifying quantities, combining coplanar vectors and resolving vectors into perpendicular components.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Covered syllabus points

1.4.1—The difference between scalar and vector quantities and give examples of1.4.2—Add and subtract coplanar vectors1.4.3—A vector as two perpendicular components

1.4 Scalars and vectors question 1

[Maximum number: 9]

Question (a)

(a)

A property of a vector quantity, that is not a property of a scalar quantity, is direction. For example, velocity has direction but speed does not.

[ 2 ]

Question (i)

(i)

State two other scalar quantities and two other vector quantities.
scalar quantities: and vector quantities: and

[ 2 ]

Question (b)

(b)

A ship at sea is travelling with a velocity of 13 ms−113 \mathrm{~ms}^{-1} in a direction 35∘35^{\circ} east of north in still water, as shown in Fig. 1.1.

Fig. 1.1

Fig. 1.1

[ 7 ]

Question (i)

(i)

Determine the magnitudes of the components of the velocity of the ship in the north and the east directions.
north component of velocity = ms−1\mathrm{ms}^{-1}
east component of velocity = ms−1\mathrm{ms}^{-1}

[ 2 ]

Question (ii)

(ii)

The ship now experiences a tidal current. The water in the sea moves with a velocity of 2.7 ms−12.7 \mathrm{~ms}^{-1} to the west.

Calculate the resultant velocity component of the ship in the east direction.
resultant east component of velocity = ms−1\mathrm{ms}^{-1}

[ 1 ]

Question (iii)

(iii)

Use your answers in (b)(i) and (b)(ii) to determine the magnitude of the resultant velocity of the ship.
magnitude of resultant velocity = ms−1\mathrm{m} \mathrm{s}^{-1}

[ 2 ]

Question (iv)

(iv)

Use your answers in (b)(i) and (b)(ii) to determine the angle between north and the resultant velocity of the ship.
angle = ∘{ }^{\circ}

[ 2 ]

1.4 Scalars and vectors question 2

[Maximum number: 2]

A car travels in a straight line up a slope, as shown in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The car has mass 850 kg and travels with a constant speed of 9.0 ms−19.0 \mathrm{~ms}^{-1}. The car's engine exerts a force on the car of 2.0 kN up the slope.

A resistive force FDF_{\mathrm{D}}, due to friction and air resistance, opposes the motion of the car.
The variation of FDF_{\mathrm{D}} with the speed v of the car is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

Consider the forces that act along the slope. Use data from Fig. 3.2 to determine the component of the weight of the car that acts down the slope.

component of weight =
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