मराठी

In a two dimensional motion, instantaneous speed v0 is a positive constant. Then which of the following are necessarily true? - Physics

Advertisements
Advertisements

प्रश्न

In a two dimensional motion, instantaneous speed v0 is a positive constant. Then which of the following are necessarily true?

पर्याय

  • The average velocity is not zero at any time.

  • Average acceleration must always vanish.

  • Displacements in equal time intervals are equal.

  • Equal path lengths are traversed in equal intervals.

MCQ

उत्तर

Equal path lengths are traversed in equal intervals.

Explanation:

Speed (Instantaneous Speed): The magnitude of the velocity at any instant of time is known as instantaneous speed or simply speed at that instant of time. It is denoted by v.

Quantitatively: Speed = Distance/Time

Mathematically, it is the time rate at which distance is being travelled by the particle.

  • Speed is a scalar quantity. It can never be negative (as shown by the speedometer of our vehicle).
  • Instantaneous speed is the speed of a particle at a particular instant of time.

Hence, Total distance travelled = Path length = (Speed) × Time taken

Important point: We should be very careful with the fact that speed is related to the total distance covered not displacement.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Motion In a Plane - Exercises [पृष्ठ २०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Physics [English] Class 11
पाठ 4 Motion In a Plane
Exercises | Q 4.7 | पृष्ठ २०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in figure. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?


On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.


For any arbitrary motion in space, state whether the following statement is true:

`"a"_"average"=["v"("t"_2) - "v"("t"_1)]/("t"_2 - "t"_1)`

(The ‘average’ stands for average of the quantity over the time interval t1 to t2)


For any arbitrary motion in space, state whether the following statement is true:

`"V"_"average"` = `(1/2)("v"("t"_1) + "v"("t"_2))`

(The ‘average’ stands for average of the quantity over the time interval t1 to t2)


For any arbitrary motion in space, state whether the following statement is true:

`"r"("t") = "r"(0) + "v"(0)"t"  + 1/2  "a"  "t"^2 `

(The ‘average’ stands for average of the quantity over the time interval t1 to t2)


Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in cartesian co-ordinates A = `A_xhati + A_yhatj` where `hati` and `hatj` are unit vector along x and y directions, respectively and Ax and Ay are corresponding components of (Figure). Motion can also be studied by expressing vectors in circular polar co-ordinates as A = `A_rhatr + A_θhatθ` where `hatr = r/r = cos θhati + sin θj` and `hatθ = - sin  θhati + cos θ hatj` are unit vectors along direction in which `r` and `θ` are increasing.

  1. Express `hati` and `hatj` in terms of `hatr` and `hatθ`
  2. Show that both `hatr` and `hatθ` are unit vectors and are perpendicular to each other.
  3. Show that `d/(dt) (hatr) = ωhatθ` where `θ = (dθ)/(dt)` and `d/(dt) (hatθ) = - ωhatr`
  4. For a particle moving along a spiral given by `t = aθhatr`, where a = 1 (unit), find dimensions of ‘a’.
  5. Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.

Two vectors `vec"A"` and `vec"B"` have equal magnitudes. If magnitude of `vec"A"` + `vec"B"` is equal to two times the magnitude of `vec"A"` - `vec"B"`, then the angle between  `vec"A"` and `vec"B"` will be :


Boat travels upstream in a river and at t = 0 a wooden cork is thrown over the side with zero initial velocity. After 7.5 minutes the boat turns and starts moving downstream catches the cork when it has drifted 1 km downstream. Then the velocity of water current is ______.


A displacement vector, at an angle of 30° with y-axis has an x-component of 10 units. Then the magnitude of the vector is ______.


A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. The height of the tower is ______.

(g = 9.8 m/s2)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×