Displacement in 2D Motion

Q. Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. 4.20. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?

Q. The velocity of a particle moving along a line is $v=t^2-5t+6$, from $t=4$ to $t=8$. What is the relation between distance $\left(S\right)$ and displacement $\left(\Delta X\right)$

1. $S>|\Delta X|$
2. $S<|\Delta X|$
3. $S=|\Delta X|$
4. $S>|\Delta X{|}^2$

Q. On an open ground, a motorist follows a track that turns to his left by an angle of 600 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.

Q. A car starts from rest and accelerates at $5{\text{m/s}}^2$. At $t=4\text{s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6\text{s}$?

$(g=10{\text{m/s}}^2)$

1. $20\text{m/s},5{\text{m/s}}^2$
2. $20\sqrt{2}\text{m/s},10{\text{m/s}}^2$
3. $20\sqrt{2}\text{m/s},0$
4. $20\text{m/s},0$

Q.

(i) Position vector $\overrightarrow{A}\left(1\right)2\hat{i}+\hat{j}$
(ii) Postion vector $\overrightarrow{B}\left(2\right)3\hat{i}+3\hat{j}$
(iii)Displacement ${\overrightarrow{d}}_{AB}\left(3\right)5\hat{i}+4\hat{j}$
(iv)Position vector of point of
intersection of path 1 & path 2 $\left(4\right)4\hat{i}+3\hat{j}$

1. (i) - (2), (ii) - (3), (iii) - (1), (iv) - (4)

2. (i) - (3), (ii) - (1), (iii) - (2), (iv) - (4)

3. (i) - (1), (ii) - (2), (iii) - (3), (iv) - (4)

4. (i) - (4), (ii) - (1), (iii) - (3), (iv) - (2)

Q. The position of a particle moving in a straight line is described by the relation $x=3+6t-t^2\text{m}$. The distance covered by the particle in metres in first $6\text{s}$ is

Q.

What are the initial position vector ${\overrightarrow{r}}_i$ and final position vector ${\overrightarrow{r}}_f$, both in unit-vector notation? What is the x component of displacement $\Delta \overrightarrow{r}$?

(i)	Position vector ${\overrightarrow{r}}_i$	(x)	$5\hat{i}-3\hat{j}-1\hat{k}$
(ii)	Postion vector ${\overrightarrow{r}}_f$	(y)	$-2\hat{i}-4\hat{j}+1\hat{k}$
(iii)	x-component of displacement $\Delta \overrightarrow{r}$	(z)	$7\hat{i}+1\hat{j}-2\hat{k}$

1. (i) - (x); (ii) - (z); (iii) - (y)

2. (i) - (z); (ii) - (x); (iii) - (y)

3. (i) - (z); (ii) - (y); (iii) - (x)

4. (i) - (x); (ii) - (y); (iii) - (z)

Q. If a projectile is projected an angle ${30}^{\circ }$ with respect to the horizontal with an initial velocity 4 m/s, range of projectile is

1. 1.26 m
2. 1.13 m
3. 0.86 m
4. 1.384 m

Q.

(i)	Position vector $\overrightarrow{A}$	(1)	$2\hat{i}+\hat{j}$
(ii)	Postion vector $\overrightarrow{B}$	(2)	$3\hat{i}+3\hat{j}$
(iii)	Displacement ${\overrightarrow{d}}_{AB}$	(3)	$5\hat{i}+4\hat{j}$
(iv)	Position vector of point of intersection of path 1 & path 2	(4)	$4\hat{i}+3\hat{j}$

1. (i) - (3), (ii) - (1), (iii) - (2), (iv) - (4)

2. (i) - (2), (ii) - (3), (iii) - (1), (iv) - (4)

3. (i) - (1), (ii) - (2), (iii) - (3), (iv) - (4)

4. (i) - (4), (ii) - (1), (iii) - (3), (iv) - (2)

Q.

(i)	Position vector $\overrightarrow{A}$	(1)	$2\hat{i}+\hat{j}$
(ii)	Postion vector $\overrightarrow{B}$	(2)	$3\hat{i}+3\hat{j}$
(iii)	Displacement ${\overrightarrow{d}}_{AB}$	(3)	$5\hat{i}+4\hat{j}$
(iv)	Position vector of point of intersection of path 1 & path 2	(4)	$4\hat{i}+3\hat{j}$

1. (i) - (3), (ii) - (1), (iii) - (2), (iv) - (4)

2. (i) - (2), (ii) - (3), (iii) - (1), (iv) - (4)

3. (i) - (1), (ii) - (2), (iii) - (3), (iv) - (4)

4. (i) - (4), (ii) - (1), (iii) - (3), (iv) - (2)

Q. The position vector of a particle is determined by the expression $\overline{r}$ = 3 $t^2$ $\hat{i}$ + 4 $t^2$$\hat{j}$ + 7$\hat{k}$ .The distance traversed in first 10 sec is

1. 500 m
2. 300 m
3. 150 m
4. 100 m

Q. In a car race, car $A$ takes $20\text{s}$ less than car $B$ to finish. It passes the finishing point with speed $v$ more than that of car $B$. Assuming that both the cars start from rest and travel with a constant acceleration of $50{\text{m/s}}^2$ and $40{\text{m/s}}^2$ respectively, what is the value of $v$ ?

1. $620\text{m/s}$
2. $894\text{m/s}$
3. $682\text{m/s}$
4. $864\text{m/s}$

Q. Find the displacement of a body as it travels to diametrically opposite point along a circle of radius 2 m.

1. 4 m
2. 3 m
3. 2 m
4. None of these

Q. The position vector of a particle is determined by the expression $\overline{r}$ = 3 $t^2$ $\hat{i}$ + 4 $t^2$$\hat{j}$ + 7$\hat{k}$ .The distance traversed in first 10 sec is

1. 500 m
2. 300 m
3. 150 m
4. 100 m

Q. Two particles A and B are moving in XY plane. Their positions vary with time $t$, according to relation
$x_A\left(t\right)=4t^2,x_B\left(t\right)=7$
$y_A\left(t\right)=3t,y_B\left(t\right)=3+4t^2$
Distance between these two particles at $t=1\text{s}$ is:-

1. $5\text{m}$
2. $3\text{m}$
3. $4\text{m}$
4. $\sqrt{12}\text{m}$