A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the

Question

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)

Accepted Answer

1. **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 .
2. **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: $v = u - gt$ .
3. **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).
4. **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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