under gravity, this acceleration, though negative, results in increase in speed. For a particle thrown upward, the same negative acceleration (of gravity) results in decrease in speed. . The zero velocity of a particle at any instant does not necessarily imply zero acceleration at that instant.
A particle may be momentarily at rest and yet have non-zero acceleration. For example, a particle thrown up has zero velocity at its uppermost point but the acceleration at that instant continues to be the acceleration due to gravity. . In the kinematic equations of motion [Eq.
( . )], the various quantities are algebraic, i.e. they may be positive or negative. The equations are applicable in all situations (for one dimensional motion with constant acceleration) provided the values of different quantities are substituted in the equations with proper signs.
. The definitions of instantaneous velocity and acceleration (Eqs. ( . ) and ( .
)) are exact and are always correct while the kinematic equations (Eq. ( . )) are true only for motion in which the magnitude and the direction of acceleration are constant during the course of motion. EXERCISES .
In which of the following examples of motion, can the body be considered approximately a point object: (a) a railway carriage moving without jerks between two stations. (b) a monkey sitting on top of a man cycling smoothly on a circular track. (c) a spinning cricket ball that turns sharply on hitting the ground. (d) a tumbling beaker that has slipped off the edge of a table.
. The position-time ( x-t ) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. . .
Choose the correct entries in the brackets below ; (a) (A/B) lives closer to the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A and B reach home at the (same/different) time (e) (A/B) overtakes (B/A) on the road (once/twice). . A woman starts from her home at . am, walks with a speed of km h – on