Advertisements
Advertisements
Question
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)
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
The particle's motion is arbitrary; the acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of a particle in space.
APPEARS IN
RELATED QUESTIONS
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:
`"V"_"average"` = [r(t2) - r(t1) ] /(t2 – t1)
For any arbitrary motion in space, state whether the following statement is true:
v (t) = v (0) + a t
(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?
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 particle of mass 10-2 kg is moving along the positive x-axis under the influence of a force F(x) = `-"K"/(2x)^2` where K = 10-2 Nm2. At time t = 0 it is at x = 1.0 m and its velocity is v = 0. The velocity of particle will be ______ m/s, when it reaches x = 0.50 m.
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)
The displacement s of a particle depends on time t according to the following relation `s = 1/3t^3 - t^2 + t`. The velocity and displacement of the particle at the instant when its acceleration is zero, are respectively ______.
