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
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