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NCERT Solutions for Class 9th Science Chapter 4 Pause and Ponder — Average speed and average velocity

Book page 53 Updated on2026-09-08

Q4.
During a family road trip, you drive 200 km north in three hours. Afterwards, you drive 200 km south in two hours. Find the average speed and average velocity for your entire trip.
Answer

Handle the two quantities separately — one uses the path, the other only the end points.

total distance travelled = 200 km + 200 km = 400 km
total time interval = 3 h + 2 h = 5 h

average speed = total distance travelled / time interval
= 400 km / 5 h = 80 km h⁻¹

For the velocity, take north as positive:

displacement = (+200 km) + (−200 km) = 0 km

average velocity = displacement / time interval
= 0 km / 5 h = 0 km h⁻¹
Why it happens: you finish exactly where you started, so the net change in position is zero — and average velocity, being displacement over time, must be zero however fast you drove. The average speed is not zero because the odometer counted all 400 km. Note also that the average speed is not the average of the two leg speeds: leg speeds are 200/3 ≈ 66.7 km h⁻¹ and 200/2 = 100 km h⁻¹, whose plain average is 83.3 km h⁻¹, not 80 km h⁻¹. Always divide total distance by total time.
In SI units: 80 km h⁻¹ = 80 × 1000 m / 3600 s = 22.2 m s⁻¹.
Q5.
Under what condition(s) is the (i) magnitude of average velocity of an object equal to its average speed? (ii) magnitude of average velocity of an object zero while its average speed is not zero?
Answer

(i) When the object moves along a straight line in one direction only, without ever turning back, during that whole time interval.

|average velocity| = |displacement| / t   and   average speed = distance / t
these are equal exactly when |displacement| = distance travelled
which happens only when the path is a straight line covered in one direction

(ii) When the object returns to its starting position at the end of the interval, so the displacement is zero, while the path length is not.

displacement = 0 → average velocity = 0
distance travelled ≠ 0 → average speed ≠ 0

Examples: Sarang in Example 4.2 swims 50 m up and back in 50 s — average speed 1 m s⁻¹, average velocity 0 m s⁻¹. So does anything completing a full revolution of a circle, or a train that returns to the same platform.

Why it happens: the numerator is the only difference between the two definitions — distance for speed, displacement for velocity. Case (i) is the situation where those two numerators coincide; case (ii) is the extreme where the displacement numerator collapses to zero while the distance numerator keeps growing.
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