# CIE AS & A Level Physics : 1.4 Scalars and vectors – Exam style question – Paper 2

### Question

(a) Complete Table 1.1 by stating whether each of the quantities is a vector or a scalar. (b) The variation with time t of the velocity v of an object is shown in Fig. 1.1. (i) Determine the acceleration of the object from time t = 0 to time t = 4.0s.
acceleration = ………………………………………… ms−2 

(ii) Determine the distance moved by the object from time t = 0 to time t = 4.0s.
distance = …………………………………………….. m 
(c) (i) Define force.                                                                                                              

(ii) The motion represented in Fig. 1.1 is caused by a resultant force F acting on the object.
On Fig. 1.2, sketch the variation of F with time t from t = 0 to t = 12.0s. Numerical values of F are not required. [Total: 10]

Ans

(a) acceleration: vector
work: scalar
power: scalar
Three correct scores 2 marks. Two correct scores 1 mark.

(b) (i) a = (v –u) / t or a = gradient or a =Δv / (Δ)t
e.g.     a = (1.40 – 0.70) / 4.0
= 0.18 ms–2

(b) (ii)  distance = 0.5× (0.70 + 1.40)× 4.0
or
(0.70× 4.0) + (0.5× 0.70× 4.0)
= 4.2 m

(c) (i) (force equal to) rate of change of momentum

(c) (ii) horizontal line starting from t = 0 and ending at t = 4.0 s at a positive value of F
horizontal line starting from t = 4.0 s and ending
at t = 8.0 s at F = 0
horizontal line starting from t = 8.0 s and ending at t = 12.0 s at a negative value of F and the magnitude of F is larger than
from t = 0 to 4.0 s

### Question

(a) State what is meant by a scalar quantity and by a vector quantity.
scalar: ……………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………
vector: ……………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………


(b) Complete Fig. 1.1 to indicate whether each of the quantities is a vector or a scalar. (c) An aircraft is travelling in wind. Fig. 1.2 shows the velocities for the aircraft in still air and for  the wind. The velocity of the aircraft in still air is 95 m s–1 to the west.
The velocity of the wind is 28 m s–1 from 65° south of east.

(i) On Fig. 1.2, draw an arrow, labelled R, in the direction of the resultant velocity of the
aircraft.                                                                                                                                                       

(ii) Determine the magnitude of the resultant velocity of the aircraft.

magnitude of velocity = …………………………………………. m s–1 

Ans:

(a) a scalar has magnitude (only)
a vector has magnitude and direction

(b) power: scalar
temperature: scalar
momentum: vector

(c)(i) arrow labelled R in a direction from 5° to 20° north of west
(c)(ii)$$v^2 = 282 + 952 – (2× 28 × 95× cos 115°)$$

or
$$v^2 = [(95 + 28cos65°)^2 + (28sin65°)^2]$$

v = 110 m s–1 (109.8 m s–1)
or (scale diagram method)
triangle of velocities drawn
v = 110 m s–1 (allow 108 –112 m s–1)

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