Due to an acceleration of 4 m/s2, the velocity of a body increases from 10 m/s to 30 m/s in a certain period. Find the displacement (in m) of the body in that period.
- A.200
- B.250
- C.100
- D.125
Correct answer
Explanation
The correct answer is C, 100. Use the third equation of motion, which links velocity and distance without needing time: v squared equals u squared plus 2as. Here u is 10 m/s, v is 30 m/s and a is 4 m/s2, so 900 equals 100 plus 8s, giving 8s equal to 800 and s equal to 100 metres. The same answer comes the long way round: the time taken is (30 minus 10) divided by 4, that is 5 seconds, and the average velocity of uniformly accelerated motion is (10 plus 30) divided by 2, that is 20 m/s, so the displacement is 20 times 5, again 100 metres. A is wrong because 200 comes from leaving out the initial velocity and taking v squared as 2as with u equal to zero. B is wrong because 250 follows no correct step here. D is wrong because 125 comes from using the wrong time of 5 seconds with a mistaken average of 25 m/s. Exam tip: the three equations are v = u + at, s = ut + half at squared, and v squared = u squared + 2as.
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