\(\mathrm{A} \rightarrow \mathrm{b} \quad\) The piston of a motorcar engine moving at uniform speed is said to be in periodic motion. \(\mathrm{B} \rightarrow \mathrm{e}, \mathrm{b} \quad\) The objects executing vibratory motion undergo change in shape or size. The piston of a motor car engine executes vibratory motion. \(\mathrm{C} \rightarrow \mathrm{g} \quad\) Body at rest will have zero speed as well as zero velocity. \(\mathrm{D} \rightarrow\) a Maximum displacement of a body from its mean position is called amplitude. \(\mathrm{E} \rightarrow \mathrm{c} \quad\) A body moving with variable speed is said to be in non-uniform motion. \(\mathrm{F} \rightarrow \mathrm{d} \quad 1 \mathrm{~ms}^{-1}=\frac{1 \mathrm{~m}}{1 \mathrm{~s}}=\frac{\frac{1}{100} \mathrm{~km}}{\frac{1}{3600} \mathrm{~h}}=\frac{18}{5} \mathrm{~km} \mathrm{~h}^{-1}\) \(\mathrm{G} \rightarrow \mathrm{f} \quad\) Average velocity \(=\frac{\text { Total displacement }}{\text { Total time }}\)

Step by step solution

01

Statement A

The piston of a motorcar engine moving at uniform speed is said to be in periodic motion. In periodic motion, an object moves in a repeated pattern over time. In this case, the piston in the engine moves up and down in a regular pattern as the engine operates.

02

Statement B

The objects executing vibratory motion undergo change in shape or size. The piston of a motor car engine executes vibratory motion. Vibratory motion refers to objects oscillating or changing their shape, size or position rapidly. The piston of a motor car engine moves up and down rapidly in its cylinder, which is an example of vibratory motion.

03

Statement C

Body at rest will have zero speed as well as zero velocity. This statement highlights the fact that when an object is at rest (not moving), it has both zero speed and zero velocity. Speed is a scalar quantity that describes how fast an object is moving, while velocity is a vector quantity that describes both the object's speed and direction of motion.

04

Statement D

Maximum displacement of a body from its mean position is called amplitude. Amplitude is an important characteristic when studying oscillating or vibrating systems, such as the piston in a motor car engine. The larger the amplitude, the greater the displacement of the object from its mean position.

05

Statement E

A body moving with variable speed is said to be in non-uniform motion. Non-uniform motion occurs when an object's speed or direction changes over time. For example, a car accelerating or decelerating, or a ball changing direction when it bounces, are examples of non-uniform motion.

06

Statement F

\(1\mathrm{~ms}^{-1}=\frac{1\mathrm{~m}}{1\mathrm{~s}}=\frac{\frac{1}{100}\mathrm{~km}}{\frac{1}{3600}\mathrm{~h}}=\frac{18}{5}\mathrm{~km}\mathrm{~h}^{-1}\). This statement is converting a speed of 1 meter per second (m/s) into kilometers per hour (km/h). To do this, you can write the conversion factors: 1 m/s is equal to \(\frac{1}{1000}\) km/s (since 1 km = 1000 m) and \(3600\) s/h (since 1 h = 3600 s). Multiplying these out, you get \(\frac{18}{5}\) km/h.

07

Statement G

Average velocity \(=\frac{\text{Total displacement}}{\text{Total time}}\). This equation defines the average velocity of an object. If you want to find the average velocity of an object, you need to divide the total displacement of the object (the change in its position) by the total time it took for the displacement to occur. Displacement is a vector, so the average velocity does consider direction.

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