Motion: 1 - UPSC Sci & Tech Free MCQ Test with solutions

• Option A: Uniform Motion - Bowling speed in km/h - Incorrect. The term "bowling speed" refers to the speed of a cricket ball, which can vary and is typically non-uniform. Uniform motion means covering equal distances in equal intervals of time, which is not necessarily the case for bowling speed.
• Option B: Non-Uniform Motion - Car moving on a crowded street - Correct. A car moving on a crowded street often has to change its speed frequently due to traffic conditions, which is a perfect example of non-uniform motion.
• Option C: Displacement - Total distance covered - Incorrect. Displacement refers to the shortest distance from the initial to the final position of an object, which is not always equal to the total distance covered.
• Option D: Reference Point - Acceleration - Incorrect. A reference point is a fixed point used to describe the position of an object, while acceleration is the rate of change of velocity.

Topic in NCERT: Non-Uniform Motion

Line in NCERT: "In our day-to-day life, we come across motions where objects cover unequal distances in equal intervals of time, for example, when a car is moving on a crowded street or a person is jogging in a park. These are some instances of non-uniform motion."

To find the velocity with which the ball will strike the ground, we can use the equations of motion under uniform acceleration. The relevant equation here is:

v²=u²+2as

where:

• v is the final velocity
• u is the initial velocity (which is 0 since the ball is gently dropped)
• a is the acceleration due to gravity (10 m/s² in this case)
• s is the distance fallen (20 m)

Substitute the known values into the equation:

v² = 0² + 2 × 10 × 20
v² = 400
v = √400
v = 20 m/s

So, the ball will strike the ground with a velocity of 20 m/s.

Topic in NCERT: Uniformly Accelerated Motion

Line in NCERT: "A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s², with what velocity will it strike the ground?"

Distance: The total distance travelled by the runner is calculated as follows:

• One full lap around the track is the circumference, given by the formula C = 2πr, where r is the radius.
• For a radius of 7 m, the circumference is approximately 43.96 m.
• Since the runner completes 2 laps, the total distance is 2 × 43.96 m = 87.92 m.

Displacement: Displacement is the shortest distance from the initial to the final position:

• After 2 laps, the runner returns to the starting point.
• Thus, the displacement is 0 m.

In summary, the total distance travelled is 87.92 m and the displacement is 0 m.

At maximum height, v = 0 m/s, u = 25 m/s, a = -10 m/s² (upward motion, gravity acts downward).

Use v² = u² + 2as

→ 0 = (25)² + 2(-10)s

→ 0 = 625 - 20s

→ s = 625 / 20 = 31.25 m.

• Statement (i) is correct. The simplest type of motion is indeed motion along a straight line, as mentioned in the provided content.
• Statement (ii) is correct. The magnitude of displacement can be equal to the distance travelled, particularly when the object moves in a straight line without changing direction.
• Statement (iii) is incorrect. The motion of a freely falling body is an example of uniformly accelerated motion, not non-uniformly accelerated motion.
• Statement (iv) is correct. The distance-time graph for uniform motion is a straight line, indicating constant speed over time.
• Therefore, the correct statements are (i), (ii), and (iv).

Circumference = 2πr = 2 × 3.14 × 5 = 31.4 m.

Time for one revolution = 4 s.

Speed = Circumference / Time = 31.4 / 4 = 7.85 m/s.

Uniform circular motion is accelerated because the direction of velocity changes continuously, even if speed is constant.

The slope of a distance-time graph represents the speed  of an object. This is because the slope is calculated as the change in distance divided by the change in time, which is the definition of speed.