Single Choice

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

A$$500\ m$$
Correct Answer
B$$300\ m$$
C$$150\ m$$
D$$100\ m$$

Solution

$$\vec r =3t^2 \hat i +4t^2 \hat j+7\hat k$$
at $$t=0, \vec r_1 =7\hat k$$
at $$t=10$$ sec, $$\vec r_2 =300\hat i+400\hat j +7\hat k$$
$$\vec {\Delta r}= \vec r_2 -\vec r_1 =300\hat i+400\hat j$$
$$|\vec {\Delta r}|=|\vec r_2 - \vec r_1|=\sqrt {(300)^2 +(400)^2} =500\ m$$

SIMILAR QUESTIONS

Kinematics

In a two dimensional motion, instantaneous speed $$ { v }_{ 0 } $$ is a positive constant. Then which of the following are necessarily true?

Kinematics

A body moves 6 m north. 8 m east and 10m vertically upwards, what is its resultant displacement from initial position (only magnitude)

Kinematics

A train covered a certain distance at a uniform speed. If the train would have been $$10$$ km/h faster, it would have taken $$2$$ hours less than the scheduled time. And, if the train were slower by $$10$$ km/h; it would have taken $$3$$ hours more than the scheduled time. Find the distance covered by the train.

Kinematics

An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.6 km, but when the snow clears, he discovers that he actually traveled 7.8 km at $$ 50^o $$ north of due east. (a) How far and (b) in what direction must he now travel to reach base camp?

Kinematics

What displacement must be added to the displacement $$25\hat i-6\hat j\ m$$ to give a displacement of $$7.0\ m$$ pointing in the $$x-$$ direction

Kinematics

While travelling from one station to another, a car travels $$75\ km$$ North, $$60\ km$$ North-east and $$20\ km$$ East. The minimum distance between the two stations is

Kinematics

The position vectors of points $$A, B, C$$ and $$D$$ are $$A=3\hat{i}+4\hat{j}+5\hat{k}, B=4\hat{i}+5\hat{j}+6\hat{k}, C=7\hat{i}+9\hat{j}+3\hat{k}$$ and $$D=4\hat{i}+6\hat{j}$$ then the displacement vectors $$AB$$ and $$CD$$ are

Kinematics

A man walks 8 m towards East and then 6 m towards North. His magnitude of displacement is

Kinematics

If A is to the south of B and C is to the east of B, in what direction is A with respect to C?

Kinematics

A body moves 6 m north. 8 m east and 10m vertically upwards, what is its resultant displacement from initial position (only magnitude)

Contact Details