Ram records the odometer readings of his car for the distance covered from 2000 km at the start of his journey and 2400 km at the end of the journey after 8 hours. What is the average speed of the car ?
- (a)50 km/h
- (b)60 km/h
- (c)70 km/h
- (d)80 km/h
Correct — A, 50 km/h. An odometer counts the distance a vehicle has actually travelled, so the distance covered on this journey is the difference between the two readings, 2400 − 2000 = 400 km. The journey took 8 hours. Average speed is total distance divided by total time, which gives 400 ÷ 8 = 50 km/h. Notice that the question tells you nothing about the route or about how fast the car was moving at any instant, and average speed needs neither.
- (b)60 km/h — At 60 km/h for 8 hours the car would have covered 480 km, so the odometer would have to read 2480 at the end rather than 2400.
- (c)70 km/h — 70 km/h over 8 hours means 560 km, which would take the odometer to 2560. The reading given does not support it.
- (d)80 km/h — 80 km/h over 8 hours means 640 km. Put another way, 400 km at 80 km/h would have taken only 5 hours, not the 8 hours stated.
Average speed is total path length divided by total time taken, and it is a scalar. Average velocity is total displacement divided by total time, and it is a vector. An odometer measures path length, not displacement, which makes it exactly the right instrument for an average-speed question and the wrong one for an average-velocity question.
Two habits protect you here. First, always subtract the two odometer readings — a candidate in a hurry can divide the final reading of 2400 by 8, and although 300 is not among the options in this particular paper, the same slip elsewhere is fatal. Second, keep speed and velocity apart. If this car had driven 200 km out and 200 km back to where it started, the odometer would still show 400 km and the average speed would still be 50 km/h, but the average velocity would be zero, because the displacement would be zero. Examiners in this series set both versions.
- Average speed equals total distance travelled divided by total time taken.
- An odometer records the distance a vehicle has covered along its actual path, not its straight-line displacement.
- 400 km in 8 hours works out to 50 km/h; the same 8 hours at 60 km/h would have needed 480 km.
- Average velocity uses displacement, so a round trip that returns to its starting point has zero average velocity however large its average speed.
Subtract the readings first, then divide by the time — that gives option (a), 50 km/h.
- Using the final odometer reading as the distance travelled instead of the difference between the two readings.
- Answering with average velocity when average speed has been asked, or the other way round.
As a one-step arithmetic item like this one, or as a two-leg journey where the two legs have different speeds and the average must be worked out properly.
A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is
- (a) 18 km/hr
- (b) 24 km/hr
- (c) 30 km/hr
- (d) 36 km/hr
Answer(a) 18 km/hr
The same definition, made harder. Total distance over total time is still the only rule you need — UPSC simply arranges the numbers so that the plain average of 10, 20 and 60 is offered as a trap.
A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed in kilometres/hour during the entire roundtrip?
- (a) 45
- (b) 20
- (c) 400/9
- (d) Impossible to find out unless the distance between the two places is known
Answer(c) 400/9
The round-trip version. Equal distances at unequal speeds give the harmonic mean, not 45, and the distance cancels out — the same total-distance-over-total-time rule doing the work.
A car starts from Bengaluru, goes 50 km in a straight line towards south, immediately turns around and returns to Bengaluru. The time taken for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip
- (a) is 0.
- (b) is 50 km/hr.
- (c) is 25 km/hr.
- (d) cannot be calculated without knowing acceleration.
Answer(a) is 0.
The companion trap from an earlier NDA paper. There the car returns to its start so the average velocity is zero while the average speed is 50 km/h; here the odometer gives the path length and average speed is what is wanted. Read which of the two words the question uses.
- practice — not a real PYQ
A cyclist covers 30 km in 2 hours and the next 30 km in 3 hours. What is his average speed for the whole trip?
- (a)10 km/h
- (b)12 km/h
- (c)12.5 km/h
- (d)15 km/h
Answer(b) 12 km/h — 60 km covered in a total of 5 hours; note that it is not the plain average of 15 and 10.
- practice — not a real PYQ
A car travels from A to B and returns to A, covering 240 km in all in 4 hours. Its average velocity for the whole trip is
- (a)60 km/h
- (b)30 km/h
- (c)zero
- (d)cannot be determined
Answer(c) zero — the car ends where it began, so the displacement is zero even though the average speed is 60 km/h.