A motorcycle has initial velocity of 5 m/s. After 3 seconds, the velocity is 7 m/s. The displacement of the motorcycle in 3 seconds is :
- A.21 m
- B.18 m
- C.36 m
- D.6 m
Correct answer
Explanation
The correct answer is B, 18 m. With the velocity changing steadily from 5 m/s to 7 m/s, the average velocity is 6 m/s, and 6 m/s × 3 s = 18 m.
For uniform acceleration, displacement s = ((u + v)/2) × t. Here u = 5 m/s, v = 7 m/s and t = 3 s, so s = (12/2) × 3 = 18 m. The same result comes from the other equation: acceleration a = (7 − 5)/3 = 2/3 m/s², and s = ut + ½at² = 15 + ½ × (2/3) × 9 = 15 + 3 = 18 m.
A is wrong because 21 m assumes the final speed of 7 m/s for the whole 3 seconds.
C is wrong because 36 m is double the correct value, as if the speeds were added without halving.
D is wrong because 6 m is only the average velocity figure, not the distance covered in 3 seconds.
Exam tip: under uniform acceleration, displacement = average of initial and final velocity × time.
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