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?
(a) Total distance travelled = 23 km
Total time taken = 28 min = `28/60 h`
∴Average speed of the taxi = `"Total distance travelled"/"Total time taken"`
= `23/(28/60) = 49.29 "km/h"`
(b) Distance between the hotel and the station = 10 km = Displacement of the car
∴Average velocity = `10/(28/60) = 21.43 "km/h"`
Therefore, the two physical quantities (averge speed and average velocity) are not equal.
Here, actual path length travelled, s = 23 km; Displacement = 10 km;
Time taken, t = 28 min = `28/60h`
(a) Average speed of taxi = `"actual path length"/"time taken" = 23/(28/60) km/h = 49.3 "km/h"`
(b)Magnitude of average velocity = `"displacement"/"time taken" = 10/(28/60) "km/h" = 21.4 "km/h"`
The average speed is not equal to the magnitude of average velocity. The two are equal for the motion of taxi along a straight path in one direction.
Read each statement below carefully and state with reasons, if it is true or false:
the total path length is always equal to the magnitude of the displacement vector of a particle.
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:
(a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.
- Scalars and Vectors