Motion in a Plane

State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.

Pick out the only vector quantity in the following list: Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

Establish the following vector inequalities geometrically or otherwise: When does the equality sign above apply?

Given a + b + c + d = 0, which of the following statements are correct:

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.

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s^-1 can go without hitting the ceiling of the hall?

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?

An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

Read each statement below carefully and state, with reasons, if it is true or false:

The position of a particle is given by r = 3.0t i - 2.$0t^{2}$ j + 4.0 k m where t is in seconds and the coefficients have the proper units for r to be in metres.

A particle starts from the origin at t = 0 s with a velocity of 10.0 j m/s and moves in the x-y plane with a constant acceleration of (8.0 i + 2.0 j) m s^-2.

i and j are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors i + j, and i - j? What are the components of a vector A = 2i + 3j along the directions of i + j and i - j? [You may use graphical method]

For any arbitrary motion in space, which of the following relations are true: (The ‘average’ stands for average of the quantity over the time interval t1 to t2)

Read each statement below carefully and state, with reasons and examples, if it is true or false: A scalar quantity is one that