1© Manhattan Press (H.K.) Ltd. 2.3 Equations of uniformly accelerated motion.

© Manhattan Press (H.K.) Ltd. 1

2.3 Equations of uniformly 2.3 Equations of uniformly accelerated motionaccelerated motion


Uniformly accelerated motion

2.3 Equations of uniformly accelerated motion (SB p. 89)


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Common Error




1. First equation of motion

Slope (m) = = a

v – u = at

tuv

v = u + at




2. Second equation of motion

Displacement (s) = Area of ABDE =2

)( tvu

222

2)(

22atutut

tatuuts

2

21 atuts




3. Third equation of motion

From the first equation, we have:

v2 = (u + at)2 = u2 + 2uat + a2t2

= u2 + 2a(ut + at2/2)

v2 = u2 + 2as

Note: All equations of motion are applicable only if an object moves with uniform acceleration.

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Example 3Example 3


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If a body moves with a constant acceleration along a straight line, it is said to have a uniformly accelerated motion.

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Uniformly accelerated motion is not the same as uniform motion. For uniformly accelerated motion, there is a change in the velocity of the object. However, there involves no change in velocity of the object in uniform motion.

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Q:Q: (a) Define acceleration.

(b) A body has an initial velocity u and an acceleration a. After a time t, the body has moved a distance s and has a final velocity v. The motion is summarised by the equations

v = u + at, s = (u + v)t.(i) State the assumption made about the

acceleration a in these equations.(ii) Use the equations to derive an expression

for v in terms of u, a and s.


21


Q:Q: (c) A photographer wishes to check the time

for which the shutter on a camera stays open when a photograph is being taken. To do this, a metal ball is photographed as it falls from rest. It is found that before the shutter opens, the ball falls 2.50 m from rest and, during the time that the shutter remains open, the ball falls a further 0.12 m, as illustrated in the figure. Assuming that air resistance is negligible, calculate

(i) the speed of the ball after falling 2.50 m,

(ii) the time to fall the further 0.12 m.[You may wish to use an equation of the form x =

(iii) The time for which the shutter stays open is marked on the camera as 1/60 s. Comment on whether the test confirms this time.

(UCLES, 1999, A Level Phys, 9248/2, November, Q2)

Solution


aacbb

242


Solution:Solution:(a) Acceleration is the rate of change of velocity with respect to time.

(b) (i) The assumption made is that the acceleration a is constant.

(ii) The first equation: v = u + at

Substitute t into the second equation:

2as = (u + v)(u – v)

2as = v2 − u2

v2 = u2 + 2as

∴ v =


auvt

auvvus )(

21

asu 22


Solution (cont’d):Solution (cont’d):

%.. 65101650

601

601-0.017

(c) (i) Falling 2.50 m from rest, speed (v) = (−ve value not applicable)

(ii) Falling a further 0.12 m,

Time to fall the further 0.12 m (t) = 0.017 s

(iii) Error =

which is not significant. The test confirms this time.


(rejected) 4451or 0170

90542)120(90544)007(007

01200079054

81921007120

21

2

2

2

2

..t

.....

t

.t.t.

t.t..

atuts

12 s m 00750281920 ...

asu 22

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1© Manhattan Press (H.K.) Ltd. 2.3 Equations of uniformly accelerated motion.

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