A bus starting from a bus-stand and moving with uniform acceleration attains a speed of 20 km/h in 10 minutes. What is its acceleration?
- (a)200 km/h²
- (b)120 km/h²
- (c)100 km/h²
- (d)240 km/h²
Correct — B, 120 km/h². Acceleration is the change in velocity divided by the time taken for that change. The bus starts from rest, so the initial speed is zero and the change in speed is the full 20 km/h. The awkward part is the time, which is given in minutes while the options are in kilometres per hour squared, so the units have to be made to agree before dividing. Ten minutes is one-sixth of an hour. Dividing 20 km/h by one-sixth of an hour is the same as multiplying by six, which gives 120 km/h². The number reads oddly because the unit is unfamiliar, but it says something quite ordinary: if this rate were kept up for a whole hour, the bus would gain 120 km/h of speed. Anyone more comfortable in SI units can convert instead — 20 km/h is about 5·56 m/s and 10 minutes is 600 s, giving roughly 0·0093 m/s², which converts straight back to 120 km/h².
- (a)200 km/h² — Comes from dividing 20 by 0·1, that is treating ten minutes as a tenth of an hour instead of a sixth.
- (c)100 km/h² — Would require the time to be a fifth of an hour, or twelve minutes. No step in the question produces that figure.
- (d)240 km/h² — Double the correct value. It is the answer to the same problem with a final speed of 40 km/h, which is the version this item was adapted from.
Acceleration is the rate of change of velocity with time, written as final velocity minus initial velocity, all divided by the time interval. Uniform acceleration means the velocity changes by equal amounts in equal intervals, which is the case here. The SI unit is the metre per second squared, but any consistent pair of units works — kilometres per hour squared simply says how much the speed in km/h changes in each hour.
The physics in this item is one line long; the marks are in the unit handling. Two conversions are possible and both are safe if carried out consistently — turn the minutes into hours and stay in kilometres, or turn everything into metres and seconds and convert at the end. What is not safe is mixing them, which is what produces the option of 200. Starting from rest is a small gift the stem makes explicit, since it removes the initial velocity from the calculation. The problem is a close reworking of a standard textbook exercise about a train that reaches 40 km/h in ten minutes, whose answer is 240 km/h² — which is exactly why 240 appears here as a distractor, and why a candidate who half-remembers the textbook rather than working the sum can walk straight into it.
- Acceleration equals the change in velocity divided by the time taken, with uniform acceleration meaning equal changes in equal intervals.
- Ten minutes is one-sixth of an hour, so dividing by it is the same as multiplying by six.
- Starting from a bus-stand means the initial speed is zero, so the change in speed is the whole 20 km/h.
- 120 km/h² is about 0·0093 m/s²; the two are the same acceleration expressed in different units.
- The three equations of motion — v = u + at, s = ut + ½at², and v² = u² + 2as — all apply only to uniformly accelerated motion.
- Treating ten minutes as 0·1 hour instead of one-sixth of an hour.
- Mixing kilometres with seconds, or metres with hours, part way through the calculation.
- Recalling the textbook version of this problem, which uses 40 km/h and answers 240 km/h².
As a single-step acceleration numerical with a unit twist, as a velocity–time graph reading, or as an application of the equations of motion to find distance or final speed.
The speed of a car travelling on a straight road is listed below at successive intervals of 1 s : Time (s) 0 1 2 3 4 Speed (m/s) 0 2 4 6 8 Which of the following is/are correct ? The car travels 1. with a uniform acceleration of 2 m/s². 2. 16 m in 4 s. 3. with an average speed of 4 m/s. Select the correct answer using the code given below :
- (a) 1, 2 and 3
- (b) 2 and 3 only
- (c) 1 and 2 only
- (d) 1 only
Answer(a) 1, 2 and 3
The same definition applied to a table of readings. Equal speed gains in equal intervals are what uniform acceleration means, and dividing the speed gained by the time taken is the identical step this question needs.
The area under the velocity-time graph for a particle moving in a straight line with uniform acceleration gives
- (a) its average velocity
- (b) its net displacement
- (c) the distance travelled by it
- (d) its average speed
Answer(b) its net displacement
The graphical reading of the same motion. Uniform acceleration draws a straight sloping line on a velocity–time graph, and where this question asks for that slope, the 2023 item asks what the area beneath it means.
- practice — not a real PYQ
A train starting from rest attains a speed of 60 km/h in 15 minutes with uniform acceleration. Its acceleration is
- (a)60 km/h²
- (b)120 km/h²
- (c)240 km/h²
- (d)900 km/h²
Answer(c) 240 km/h² — fifteen minutes is a quarter of an hour, so 60 divided by one quarter gives 240.
- practice — not a real PYQ
A car moving at 18 m/s is brought to rest in 6 s. Its acceleration is
- (a)3 m/s²
- (b)−3 m/s²
- (c)108 m/s²
- (d)−108 m/s²
Answer(b) −3 m/s² — the velocity falls by 18 m/s in 6 s, and the minus sign marks retardation.