Motion in a Straight Line: Important Questions

Very Short Answer Questions [1 Mark Questions]

Ques. Two balls of varying masses are launched vertically upward at the same speed. Which one will reach the highest point?

Ans: If two balls with different masses are hurled vertically upward at the same speed, they will both rise to a larger height.

Ques. Isn't all uniform motion along a straight line?

Ans: Uniform motion is defined as the motion of an item travelling in a straight line at a constant velocity. It travels the same distance in the same amount of time, regardless of the length of time.

Ques. From New Delhi railway station to Vadodara, a 400-meter-long railway train is running. Is it possible to think of a train as a point object?

Ans: Yes, a railway train is considered a point object. This is due to the train's shorter length in comparison to the distance between New Delhi and Vadodara.

Ques. For uniform linear motion, what is the shape of the displacement time graph?

Ans: For homogeneous linear motion, the displacement time graph has the shape of a straight line inclined to the time axis (x-axis).

Ques. When will the magnitude of a moving object's displacement and distance be the same?

Ans: When an object is moving on a straight line, both distance and displacement are equal in magnitude.

Ques. Under what circumstances is the relationship s = vt valid?

Ans: When a particle moves at a constant speed and in a straight path, the formula s = vt stands true.

Ques. Is it possible for an object's speed to be negative? Justify. 

Ans: An object's speed can never be negative. This is due to the fact that the distance is always positive.

Short Answer Questions [2 Marks Questions]

Ques. Prove that a particle's average velocity over a time interval is either less than or equal to the particle's average speed over the same time span.

Ans: The ratio of total displacement to total time is known as average velocity. The ratio of the total distance to total time is the definition of average speed. The average velocity is less than or equal to the average speed because displacement is less than or equal to distance.

Ques. The rate at which velocity changes is known as acceleration. Assume the rate of change of acceleration is abbreviated as SLAP. After that, what is the SLAP unit? (2 Marks)

Ans: SLAP is given as Acceleration / time

Hence its unit is ms⁻³

Instantaneous SLAP is equal to Limiting Value of average SLAP

= t0 a/t = da/dt

Ques. A ball thrown upward reaches a certain height before crashing to the ground. Which of the following statements about displacement, velocity, and acceleration is correct? 

1. It fluctuates over time but never changes the sign.
2. It varies continually, with the maximum being zero at the top in the beginning.
3. It does not change throughout the travel.
4. The indicator only changes when the ball reaches the top.

Ans: Because displacement varies from start to finish, statement (a) holds true.

• Statement (b) is true for velocity because it is greatest when the ball is projected and decreases to zero at the highest point, i.e. the top.
• For acceleration, statement (c) holds true because it is constant throughout the voyage and equal to 'g'.

Ques. Is it possible for a body to be both at rest and in motion? Explain. 

Ans: Rest and motion are both relative words. A body at rest in relation to one thing may be in motion in relation to another object, for example, a person seated in a moving train is at rest in relation to other passengers in the train but in motion in relation to the surroundings (trees or buildings) on the trackside.

Ques. Separate the following in one, two, and three dimensions using one, two, and three-dimensional motions:

1. On a windy day, a kite is flying.
2. a crawling insect on a globe
3. a carrom coin rebounding from the board's edge
4. a planet that orbits its star.
5. a boat's movement.
6. the motion of a body that has been dropped.
7. the tennis ball's motion.
8. a charged particle in motion under the influence of an electric field.
9. the movement of a saw as it cuts wood.
10. molecular motion 
11. a charged particle in motion in the presence of a magnetic field.

Ans: One dimensional motion : (e), (f), (i)

Two dimensional motion : (b), (c), (d), (g), (h), (k).

Three dimensional motion : (a), (j).

Ques. When it comes to instantaneous velocity and magnitude of velocity, no distinction is necessary. The magnitude of instantaneous velocity is always equal to the instantaneous speed. Why?

Ans: We know that the first derivative of distance with respect to time is instantaneous velocity. The time period is so short in this case that it is presumed that the particle does not change its motion direction. As a result, in this time interval, both the total path length and the magnitude of displacement become equal. As a result, instantaneous velocity is always equal to instantaneous speed.

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Long Answer Questions [3 Marks Questions]

Ques. On a straight road, a car travelling at 60 km h⁻¹ outruns a scooter travelling at 40 km h⁻¹. If the scooter is in front of the car, how would the relative velocity change?

Ans: Speed of the car, V_c = 60 km/hr

Speed of the scooter, V_s = 40 km/hr

Relative velocity of the car with respect to scooter = V_cs

= V_c – V_s

= 60 – 40

= 20 km/hr

As a result, we infer that the relative velocity magnitude is the same in both circumstances, but the relative velocity direction is reversed if the scooter is ahead of the car.

Ques. "The direction of motion of a body is determined by velocity rather than acceleration." Justify this statement with an appropriate example. 

Ans: The direction of velocity is always in the same direction as the body's motion, whereas the direction of acceleration is not always in the same direction as the body's motion. As a result, we can deduce that the direction of motion of the body is determined by its velocity.

When a ball is thrown vertically upwards, for example, the ball's direction of motion and velocity are both vertically upwards. The acceleration due to gravity on the ball, on the other hand, operates vertically downwards, in the opposite direction of the ball's motion.

Ques. What are the most significant aspects of uniform motion?

Ans: The following are some key points to remember about uniform motion:

• In uniform motion, the velocity is independent of the time interval (t_{2 – 1}).
• In uniform motion, the velocity is independent of the origin.
• In uniform motion, the average and instantaneous velocities have the same value.
• There is no force acting on a uniformly moving item.
• When an object goes toward the right of the origin, velocity is positive, and when it moves toward the left of the origin, velocity is negative.

Ques. Define free fall.

Ans: Under the effect of gravity, an object released near the Earth's surface is driven downward. The magnitude of gravity's acceleration is indicated by the letter g. The object is considered to be in free fall if air resistance is ignored. If the object's height is tiny in comparison to the radius of the earth, g can be assumed to be constant, equal to 9.8 m s⁻². As a result, free fall is a uniformly accelerating motion. Because we chose the upward direction as positive, we assume that the motion is in the y-direction, or more accurately in the –y-direction.

Ques. What is a linear actuator?

Ans: In contrast to the circular motion of a standard electric motor, a linear actuator creates motion in a straight line. Linear actuators are utilised in machine tools and industrial machinery, as well as computer peripherals like disc drives and printers, valves and dampers, and a variety of other applications where linear motion is required. Linear motion is fundamental in hydraulic and pneumatic cylinders. A rotating motor can generate linear motion through a variety of processes.

Very Long Answer Questions [5 Marks Questions]

Ques. Write a short note on Reciprocating Motion? 

Ans: A repeating up-and-down or back-and-forth linear motion is known as reciprocating motion. It's used in a variety of mechanisms, including reciprocating engines and pumps. Strokes are the two opposing motions that make up each reciprocation cycle. Circular motion can be converted to reciprocating motion using a crank, and reciprocating motion can be converted back to circular motion using a crank.

Within an internal combustion engine (a form of the reciprocating engine), for example, the expansion of burning fuel in the cylinders periodically pulls the piston down, turning the crankshaft through the connecting rod. The piston is driven back up by the crankshaft's continued rotation, preparing for the next cycle.

A pump piston's reciprocating motion is similar to, but not identical to, sinusoidal simple harmonic motion. The point on the crankshaft that connects to the connecting rod revolves smoothly at a constant velocity in a circle if the wheel is driven at a perfect constant rotational rate. As a result, the displacement of that point is, by definition, sinusoidal. The angle of the connecting rod, on the other hand, changes continually throughout the cycle. As a result, the horizontal displacement of the connecting rod's "far" end (i.e., the end linked to the piston) differs significantly from sinusoidal. Circumstances in which the wheel is not spinning at a perfect constant rotational velocity, such as when a steam locomotive starts up from a stop, are far from sinusoidal.

Ques. Explain the inertial frame of reference?

Ans: An inertial frame of reference is a frame of reference that does not accelerate in classical physics or special relativity. A physical object with zero net force acting on it moves with a constant velocity in an inertial frame of reference, or, equivalently, it is a frame of reference in which Newton's first law of motion holds. In analytical terminology, an inertial frame of reference is a frame of reference that describes time and space homogeneously, isotropically, and time independently. In a theoretical sense, the physics of a system in an inertial frame has no external sources. Inertial reference frames, inertial frames, Galilean reference frames, and inertial space are all terms used to describe an inertial frame of reference.

With regard to one another, all inertial frames move in a constant, rectilinear motion; an accelerometer moving with any of them would report zero acceleration. A simple transformation can transfer measurements taken in one inertial frame to measurements taken in another (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, a set of inertial frames that roughly characterise any location small enough for the curvature of spacetime and tidal forces to be negligible can be found.

Ques. Define Circular Motion (5 Marks)

Ans: Circular motion is defined as the movement of an object around the circumference of a circle or the rotation of an item around a circular route in physics. It can be uniform, with a fixed angular rate of rotation and speed, or non-uniform, with a variable rate of rotation. A three-dimensional body rotates around a fixed axis, causing its pieces to move in circles. The movement of a body's centre of mass is described by its equations of motion. The distance between the body and a fixed point on the surface does not change when moving in a circular motion. 

A ceiling fan's blades revolving around a hub, a stone connected to a rope and swung in circles, a car turning through a curve on a racing track, an electron travelling perpendicular to a uniform magnetic field, are all examples of circular motion. The moving item is being accelerated by a centripetal force in the direction of the centre of rotation because the object's velocity vector is constantly changing direction. Newton's laws of motion state that if the item did not accelerate, it would move in a straight path.

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