Which is the incorrect formula for a body accelerating uniformly?

To identify the incorrect formula, we must look at the standard equations of uniformly accelerated motion (often called the equations of kinematics).

1. Analyze the Concepts

For a body moving with uniform acceleration ($a$), initial velocity ($u$), final velocity ($v$), time ($t$), and displacement ($s$), the standard equations are:

1. $v = u + at$
2. $s = ut + \frac{1}{2}at^2$
3. $v^2 = u^2 + 2as$
4. $s = (\frac{u + v}{2})t$

2. Evaluate the Options

• Option B ($v^2 = u^2 + 2as$): This is a standard kinematic equation. It is correct.
• Option C ($s = ut + \frac{1}{2}at^2$): This is the standard equation for displacement under uniform acceleration. It is correct.
• Option D ($v^2 - u^2 = 2as$): If you rearrange Option B by subtracting $u^2$ from both sides, you get $v^2 - u^2 = 2as$. This is mathematically identical to Option B. It is correct.
• Option A ($a = v^2 - \frac{u^2}{2}$): Let's test the dimensions and the algebra. If we rearrange the correct equation $v^2 = u^2 + 2as$ to solve for $a$: $v^2 - u^2 = 2as$ $a = \frac{v^2 - u^2}{2s}$ Comparing this to Option A, we see that Option A is missing the displacement ($s$) in the denominator and is dimensionally inconsistent. Therefore, it is the incorrect formula.

3. Conclusion

As shown in the derivation above, the acceleration $a$ must be divided by the displacement $s$ for the formula to be physically and mathematically correct.

Exam Tip

When dealing with kinematic equations in JAMB, always remember the "SUVAT" variables: S (displacement), U (initial velocity), V (final velocity), A (acceleration), and T (time). Every standard equation must contain a combination of these variables that is dimensionally consistent. If you see a formula missing a key variable like $s$ or $t$ where it should be, it is likely the "incorrect" one!