The question asks to identify the correct definition or example of a 'least count' error in measurement. We need to understand what least count means in the context of measuring instruments and how it relates to measurement errors.
This question tests knowledge of the fundamental equations of motion (kinematic equations) for uniformly accelerated motion. We need to identify the correct relationship between final velocity (v), initial velocity (u), acceleration (a), and time (t).
Correct Option: D) The equation \(v = u + at\) correctly relates final velocity (v), initial velocity (u), acceleration (a), and time (t) for an object undergoing uniformly accelerated motion in a straight line. This is derived directly from the definition of constant acceleration.
This question tests knowledge of the fundamental kinematic equations for uniformly accelerated straight-line motion. These equations relate displacement, initial velocity, final velocity, acceleration, and time. We need to identify the correct equation that specifically relates displacement (\(s\)), initial velocity (\(u\)), time (\(t\)), and acceleration (\(a\)).
C) \(s = ut + \frac{1}{2}at^2\)
This is the standard kinematic equation used to calculate displacement (\(s\)) when initial velocity (\(u\)), time (\(t\)), and uniform acceleration (\(a\)) are known.
The question asks for the third equation of motion, which relates final velocity (\(v\)), initial velocity (\(u\)), acceleration (\(a\)), and displacement (\(s\)) without directly involving time (\(t\)). We need to identify the correct formula from the given options.
The three fundamental equations of motion for uniformly accelerated linear motion are:
These equations are derived from the definitions of acceleration and average velocity under constant acceleration.
To derive the third equation from the first two:
C) \(v^2 = u^2 + 2as\) is the correct third equation of motion, which relates final velocity, initial velocity, acceleration, and displacement without involving time.
The question asks about the acceleration acting on a ball thrown vertically upward, ignoring air resistance. This scenario is a classic example of motion under gravity. We need to determine the direction and magnitude of acceleration throughout the ball's flight.
Correct Option: A) Acceleration due to gravity, acting downward at all times, with magnitude \(g \approx 9.8 \text{ m/s}^2\)
The question asks what the area under a velocity-time (v-t) graph represents for an object undergoing uniformly accelerated motion. We need to recall the fundamental definitions of velocity, displacement, and acceleration and how they relate to graphical representations.
Correct Option: D) The displacement of the object