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
Correct answer
Explanation
The correct answer is B, its net displacement. Velocity multiplied by time is displacement, so the area between a velocity-time graph and the time axis gives the displacement.
On a velocity-time graph, a small strip of width Δt under the curve has an area equal to v × Δt, which is the small displacement in that time. Adding all the strips gives the total, or net, displacement. Area above the time axis counts as positive and area below it as negative, because velocity has direction; this is why the area gives net displacement rather than distance. For uniform acceleration the graph is a straight line, so the area is a simple trapezium: s = ut + ½at².
A is wrong: average velocity is net displacement divided by time, not the area itself.
C is wrong: distance would need the areas below the axis to be added as positive, which a signed area does not do.
D is wrong: average speed is distance divided by time.
Exam tip: area under v–t graph = displacement; slope of v–t graph = acceleration; slope of x–t graph = velocity.
Practice Questions
View allConsider the following animals :
1. Hedgehog
2. Marmot
3. Pangolin
To reduce the chance of being captured by predators, which of the above organisms rolls up/roll up and protects/protect its/their vulnerable parts?
- A.1 and 2
- B.2 only
- C.3 only
- D.1 and 3
Show answer
Hedgehogs and pangolins curl into a tight ball when threatened, covering the soft belly and face with spines or scales; marmots do not.
Read the full explanation →Which one of the following is used in preparing a natural mosquito repellent?
- A.Congress grass
- B.Elephant grass
- C.Lemongrass
- D.Nut grass
Show answer
Lemongrass and its close relative citronella grass yield aromatic oils that keep mosquitoes away, so they are the base of many natural repellents.
Read the full explanation →Which one of the following devices is non-ohmic ?
- A.Conducting copper coil
- B.Electric heating coil
- C.Semi conductor diode
- D.Rheostat
Show answer
A diode does not obey Ohm's law: the current through it is not proportional to the voltage across it. An ohmic conductor gives a straight-line graph of current against voltage, so its resistance stays constant at a fixed temperature.
Read the full explanation →What is the formula mass of anhydrous sodium carbonate? (Given that the atomic masses of sodium, carbon and oxygen are 23 u, 12 u and 16 u respectively)
- A.286 u
- B.106 u
- C.83 u
- D.53 u
Show answer
Anhydrous sodium carbonate is Na₂CO₃, and 2 × 23 + 12 + 3 × 16 = 106 u. Formula mass is the sum of the atomic masses of all the atoms in one formula unit of an ionic compound.
Read the full explanation →Which one of the following minerals is used as a fuel in nuclear power stations ?
- A.Bauxite
- B.Quartz
- C.Feldspar
- D.Pitchblende
Show answer
Pitchblende, or uraninite, is the chief ore of uranium, the fuel used in most nuclear power stations. Pitchblende is a heavy, black mineral made mostly of uranium oxide.
Read the full explanation →