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velocity of \( 12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \). 4.1 Write down its velocity (magnitude and direction) at time 4.1.1 \( t_{1} \) 4.1.2 \( t_{2} \) 4.1.3 \( t_{3} \) 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 Scanned with.

Ask by Dickson Allan. in South Africa
Mar 13,2025

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At any time \( t_1 \), \( t_2 \), and \( t_3 \), the object has a velocity of \( 12 \, \mathrm{m/s} \) upwards. The velocity-time graph is a horizontal line at \( 12 \, \mathrm{m/s} \) when upwards is positive and at \( -12 \, \mathrm{m/s} \) when downwards is positive. The acceleration-time graph is a horizontal line at \( 0 \, \mathrm{m/s}^2 \) since the velocity is constant.

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The Deep Dive

Understanding velocity is more than just numbers; it's about direction! When we say the velocity is \( 12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \), it’s crucial to specify direction. For time \( t_1 \), \( t_2 \), and \( t_3 \), if the object is moving upwards, you’d state the velocity as \( 12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \uparrow \). If it's moving downwards, it becomes \( 12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \downarrow \). It’s all about clarity, folks! Now, let’s talk about those graphs! For a velocity-time graph with upwards as positive, your line would sit neatly at \( +12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \). Flip it for downwards, and YIKES, that line dives to \( -12 \mathrm{~m} \cdot \mathrm{~s}^{-1} \). Lastly, for the acceleration-time graph, since you’re dealing with gravity (which is down), you’d see a flat line at \( -9.81 \mathrm{~m/s}^2 \). Graphs aren’t just for math nerds; they’re like the art of physics!

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