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4 The position-time graph in Figure 12 shows the motion an object that has been thrown vertically upwards with a velocity of \( 12 \mathrm{~m} . \mathrm{s}^{-1} \). 4.1 Write down its velocity (magnitude and direction) at time 4.1.1 \( t_{1} \) 4.1.2 \( \quad t_{2} \) 4.1.3 \( \quad t_{3} \) 4.2 Draw the following rough sketches of the object's motion 4.2.1 velocity-time graph taking upwards as the positive direction. 4.2.2 velocity-time graph taking downwards as the positi direction. 4.2.3 acceleration-time graph taking upwards as the posi direction. (Remember that the object's acceleration constant, g.) Answers to numerical questions 2.3.1 \( 6,13 \mathrm{~m} \) above the player's hand; \( 366,15 \mathrm{~m} \) to \( 66,29 \mathrm{~m} \) (depending on roundir

Ask by Cook Munoz. in South Africa
Mar 13,2025

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At time \( t_1 \), the velocity is \( 12 - 9.81 \times t_1 \) m/s upwards. At \( t_2 \), the velocity is 0 m/s at the peak. At \( t_3 \), the velocity is \( 12 - 9.81 \times t_3 \) m/s downwards. For the velocity-time graph with upwards as positive, it starts at 12 m/s and decreases to 0 m/s at \( t_2 \), then becomes negative as the object falls. For the velocity-time graph with downwards as positive, it starts at -12 m/s and increases to 0 m/s at \( t_2 \), then becomes positive as the object falls. The acceleration-time graph is a horizontal line at -9.81 m/s².

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The Deep Dive

When an object is thrown upwards, gravity constantly acts against it, resulting in a decrease in its velocity until it reaches the peak of its flight. At \( t_1 \), the object is still ascending, so its velocity is positive, while at \( t_2 \), it has reached its peak, where its velocity is zero. Finally, at \( t_3 \), the object is descending, and its velocity takes on a negative value, but its magnitude is still less than the initial velocity of \( 12 \, \text{m/s} \) due to the effects of gravity. In sketching the velocity-time and acceleration-time graphs, it’s crucial to remember that the velocity graph will dip below the time axis when the object begins to fall, indicating a change in direction. The acceleration will remain constant at \( -9.81 \, \text{m/s}^2 \) (downwards), reflecting the consistent pull of gravity throughout the object's entire motion. Be sure to accurately represent the velocity decreasing as the object rises and increasing as it falls!

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