A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)
A
a
B
b
C
c
D
d
Step-by-Step Solution
Constant Acceleration: When a ball is thrown vertically upwards, it moves under the influence of gravity alone (neglecting air resistance). The acceleration due to gravity (g) is constant and acts downwards throughout the motion .
Equation of Motion: Taking the upward direction as positive, the initial velocity is +u and acceleration is −g. The velocity at any time t is given by the first equation of motion: v=u−gt .
Graphical Representation: The equation v=u−gt represents a straight line in a velocity-time (v−t) graph. The slope of this line is −g (constant negative slope), and the y-intercept is +u (initial velocity).
Motion Analysis: The velocity starts at a positive value, decreases linearly to zero (at maximum height), and then becomes negative as the ball falls back down, maintaining the same straight-line slope. A graph depicting a straight line with a constant negative slope is the correct representation.
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