Advertisements
Advertisements
प्रश्न
For any arbitrary motion in space, state whether the following statement is true:
`"V"_"average"` = [r(t2) - r(t1) ] /(t2 – t1)
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
This equation can represent the particle's arbitrary motion.
APPEARS IN
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.
In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
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)
In a two dimensional motion, instantaneous speed v0 is a positive constant. Then, which of the following are necessarily true?
In a two dimensional motion, instantaneous speed v0 is a positive constant. Then which of the following are necessarily true?
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.
- Express `hati` and `hatj` in terms of `hatr` and `hatθ`
- Show that both `hatr` and `hatθ` are unit vectors and are perpendicular to each other.
- Show that `d/(dt) (hatr) = ωhatθ` where `θ = (dθ)/(dt)` and `d/(dt) (hatθ) = - ωhatr`
- For a particle moving along a spiral given by `t = aθhatr`, where a = 1 (unit), find dimensions of ‘a’.
- Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.
Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms-1. [use g = 10 ms -2]:
A small toy starts moving from the position of rest under constant acceleration. If it travels a distance of 10 minutes, the distance travelled by the toy in the next will be ______.
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 :
A person can throw a ball up to a maximum range of 100 m. How high above the ground he can throw the same ball?
The position of a particle is x - y plane is described by the variables x = at3 and y = 2at. Then the acceleration of the particle ______.
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)
