A man walks 4 m east, then 3 m north. (i) What distance has he travelled?
(ii) What is his displacement from his original position?
SAMPLE ANSWER 2D
(i) He has travelled a distance of 4 3 7 m. (ii) His displacement can be found by drawing a right-angled triangle as illustrated in Fig 2.16:
Using Pythagoras’ theorem,we get: Using basic trigonometry,we get: Therefore his displacement is 5 m at 36.8 north of east.
tan
Opposite Adjacent 3
Velocity
VELOCITY Velocity (v or u) is the rate of change of displacement with respect to time.4
It is a vector quantity with an SI unit of metre per second (m s1). velocity =
displacement time
The speed of a body is the magnitude of its velocity.
In many of our numeric calculations we refer to initial velocity (u) and final velocity (v) as being the velocities at the start and end of the question. average velocity
initial velocity + final velocity 2
= u + v 2
SAMPLE PROBLEM 2E A body travels 80 m west in 20 s.What is its velocity?
4Using calculus notation, velocity is defined as:
v ds dt
VELOCITY
v s t
v velocity s displacement t time
s 442 32 225 5. 4Q tan13 4 36.8°. 4 m Fig 2.16 s 3 m
