Question

position of particle varies with time as x=(t square -3t×4)m magnitude of its average velocity in first 2s is​

Answer 1

Explanation:

negative sign indicates the direction of

displacement. Thus, it is not necessary to use

vector notation for discussing motion of objects

in one-dimension.

The magnitude of displacement may or may

not be equal to the path length traversed by

an object. For example, for motion of the car

from O to P, the path length is +360 m and the

displacement is +360 m. In this case, the

magnitude of displacement (360 m) is equal to

the path length (360 m). But consider the motion

of the car from O to P and back to Q. In this

case, the path length = (+360 m) + (+120 m) = +

480 m. However, the displacement = (+240 m) –

(0 m) = + 240 m. Thus, the magnitude of

displacement (240 m) is not equal to the path

length (480 m).

The magnitude of the displacement for a

course of motion may be zero but the

corresponding path length is not zero. For

example, if the car starts from O, goes to P and

then returns to O, the final position coincides

with the initial position and the displacement

is zero. However, the path length of this journey

is OP + PO = 360 m + 360 m = 720 m.

Motion of an object can be represented by a

position-time graph as you have already learnt

about it. Such a graph is a powerful tool to

represent and analyse different aspects of

motion of an object. For motion along a straight

line, say X-axis, only x-coordinate varies with

time and we have an x-t graph. Let us first

consider the simple case in which an object is

stationary, e.g. a car standing still at x = 40 m.

The position-time graph is a straight line parallel

to the time axis, as shown in Fig. 3.2(a).

If an object moving along the straight line

covers equal distances in equal intervals of

time, it is said to be in uniform motion along a

straight line