A body starts with an initial velocity of 20 m/s and moves with a uniform acceleration, a, for 15 seconds…

Analyze the question: We have an initial velocity u = 20 m/s, uniform acceleration a, and time t = 15 s. We need the distance S.

Concept: For uniform acceleration, the second equation of motion gives the distance:

S = ut + ½at²

Solution:

1. Substitute u = 20 and t = 15: S = (20)(15) + ½ · a · (15)²

2. Calculate each term: • ut = 20 × 15 = 300 • ½at² = ½ · a · 225 = 225a/2

3. Combine: S = 300 + 225a/2

Check the options:

• A: 56(a/2) is wrong because 56 is not 15² (225).
• B: 300 + 225a/2 matches our result.
• C: 225/(2a) puts a in the denominator, which is wrong.
• D: 300a + 225/2 puts a on the wrong term.

Tip: When you see "initial velocity, acceleration, time, find distance," go straight to S = ut + ½at². Substitute carefully, and remember to square the time (15² = 225) before multiplying by ½ and a.