NECO 2001 Physics · Question 43

A body whose initial velocity is u is uniformly accelerated to a final velocity v in t seconds. If the…

Question

A body whose initial velocity is u is uniformly accelerated to a final velocity v in t seconds. If the distance travelled is s, and the acceleration is a, which equation is INCORRECT for the motion of the body?

A.s = ut+ $\frac{1}{2}$ at2
B.v2 = u2 + 2as
C.v =u + at
D.v = u + 2as
E.s = $\frac{1}{2}$ (u+v)t

Answer: D. v = u + 2as

Explanation written with AI and checked against the answer key

Analyze the question: We need the equation that is NOT a valid equation of uniformly accelerated motion. These are the standard equations of motion, so we check each option against them.

Concept: For uniform acceleration, the three main equations of motion are:

v = u + at
s = ut + ½at²
v² = u² + 2as

There is also the average-velocity form: s = ½(u + v)t.

Checking each option:

A. s = ut + ½at² is correct (second equation of motion).
B. v² = u² + 2as is correct (third equation of motion).
C. v = u + at is correct (first equation of motion).
D. v = u + 2as is incorrect. It fails a dimensional check. Velocity v has units m/s, but 2as has units (m/s²)(m) = m²/s². You cannot add m/s to m²/s². The correct form is v² = u² + 2as, with the squares.
E. s = ½(u + v)t is correct. Since the acceleration is uniform, the average velocity is (u + v)/2, and distance = average velocity × time.

Answer: The incorrect equation is D.

Tip: When a question asks for the wrong equation, check the units (dimensional analysis). Every term added together must have the same units. This also quickly catches missing squares, such as the one in option D. Remember that the equation without time, v² = u² + 2as, always has squared velocities.

AI can make mistakes. Report anything that looks wrong.