A body having uniform acceleration a increases its velocity from u to v in time t. Which expression would not give a correct value for the body’s displacement during time t?

Question 6

A body having uniform acceleration a increases its velocity from u to v in time t.

Which expression would not give a correct value for the body’s displacement during time t?

A ut + ½ at²

B vt – ½ at²

C (v+u)(v–u) / 2a

D (v–u)t / 2

Reference: Past Exam Paper – June 2015 Paper 11 Q9

Solution:

Answer: D.

Let the displacement be s.

Since the body is undergoing uniform acceleration, we can use the equations of uniformly accelerated motion.

Consider the equation: s = ut + ½ at²             eqn (1)             [A is correct]

We know that for uniform acceleration,

v = u + at         giving u = v – at          eqn (2)

Replace equation (2) in equation (1).

s = (v – at)t + ½ at² = vt – at² + ½ at² = vt – ½ at²     since    – at² + ½ at² = – ½ at²

[B is correct]

Consider the other equation: v² = u² + 2as

Make s the subject of formula

s = v² – u² / 2a = (v+u)(v–u) / 2a                     since v² – u² = (v+u) (v–u)

[C is correct]

The only choice that remains is D and this is incorrect (we will not be able to show this equation as it is not correct).

Choice D would have been correct if there was a positive sign instead. That is, (v+u)t / 2

For uniform acceleration,

Average speed, <v> = (v + u) / 2

Speed = distance / time           giving distance = <v> × t = (v+u)t / 2