Lakhmir Singh & Manjit Kaur Test: Motion - Free MCQ with solutions

Vector Quantity

• Direction: A vector quantity has a specific direction in space. This means that not only does it have a magnitude, but it also has a specific orientation or direction in which it is pointing.
• Magnitude: In addition to having a direction, a vector quantity also has a magnitude. This magnitude represents the size or strength of the vector, indicating how much of the quantity is present.
• Both Magnitude and Direction: Therefore, a vector quantity possesses both magnitude and direction, distinguishing it from scalar quantities which only have magnitude. This dual nature of vectors allows for a more detailed description of physical quantities.

Topic in NCERT: SPEED WITH DIRECTION
Line in NCERT: "The quantity that specifies both these aspects is called velocity."

• Odometer of automobiles records distance travelled.
• The primary function of an odometer in automobiles is to measure and display the total distance the vehicle has traveled since it was first put into use.
• This distance is usually displayed in kilometers or miles depending on the unit system used in the region.

Topic in NCERT: Example 7.2

Line in NCERT: "The odometer of a car reads 2000 km at the start of a trip and 2400 km at the end of the trip."

Speedometer Measurement

• Instantaneous Speed: The speedometer of a car measures the instantaneous speed at any given moment.
• It provides a real-time reading of how fast the car is moving at that particular moment.
• This measurement is important for drivers to ensure they are following speed limits and driving safely.
• It helps drivers make adjustments to their speed based on road conditions, traffic, and other factors.

• A displacement–time graph shows how displacement changes with time.

• If the graph is parallel to the time axis, it means that displacement is not changing over time.

• This implies the particle is not moving, i.e., displacement is constant.

• Velocity = change in displacement / time
  Since displacement doesn't change, the numerator is zero, so:

• Velocity = Displacement/ Time = 0/Time = 0

• Displacement is the straightest shot (shortest distance) between start and end.
• Distance is the total path taken.
• Imagine going for a walk around a block - the displacement is the length of one side, while the distance is the entire walk.
• The numerical ratio of displacement to distance is calculated as displacement divided by distance.
• So the ratio:
• Can be 1 (straight path)
• Is less than 1 (curved path or going back and forth)
• Never more than 1

Therefore, the answer is D: equal to or less than 1.

Topic in NCERT: MOTION ALONG A STRAIGHT LINE

Line in NCERT: "The magnitude of displacement (35 km) is not equal to the path length (85 km)."

• Displacement is the straight line distance between the starting and ending points of an object's motion.
• In this scenario, the body starts at A, goes to B, and then returns to A. Even though the body travels a certain distance (twice the distance between A and B), it ends up back at its starting point (A).
• Since displacement considers the net change in position, and the body ends at the same point it started, the displacement is zero.

Topic in NCERT: Motion Along a Straight Line

Line in NCERT: "the final position coincides with the initial position, and therefore, the displacement is zero."

• In a distance-time graph, the slope or gradient. The greater the gradient, the greater the rate of change.
• The line is equal to the speed of the object.
• The steeper the line (and the greater the gradient) , the faster the object is moving.

On a distance–time graph, distance is on the vertical axis and time is on the horizontal axis. The slope indicates how rapidly the distance changes over time. If the line rises quickly (steeply), it means that more distance is covered in less time, indicating a higher speed. A flat line shows distance is not changing, so the object is not moving. A gentle slope shows distance increases slowly, meaning a slower speed. A steep slope shows distance increases quickly, meaning a faster speed. A curved line shows that the slope itself is changing, which means accelerated motion. Therefore, a steep slope indicates faster motion.

Topic in NCERT: DISTANCE–TIME GRAPHS

Line in NCERT: "Thus, the graph shown in Fig. 7.4 indicates that a steep slope represents faster motion."

• Option B is correct because Car B has the flattest slope in its distance-time graph, indicating it covers the least distance in a given time and thus is the slowest among the four cars.