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

2 © Manhattan Press (H.K.) Ltd. Uniformly accelerated motion 2.3 Equations of uniformly accelerated motion (SB p. 89) Uniformly accelerated motion Go to More to Know 2 More to Know 2 Go to Common Error

3 © Manhattan Press (H.K.) Ltd. Uniformly accelerated motion 2.3 Equations of uniformly accelerated motion (SB p. 89) 1. First equation of motion Slope (m) = = a v – u = at v = u + at

4 © Manhattan Press (H.K.) Ltd. Uniformly accelerated motion 2.3 Equations of uniformly accelerated motion (SB p. 89) 2. Second equation of motion Displacement (s) = Area of ABDE =

5 © Manhattan Press (H.K.) Ltd. Uniformly accelerated motion 2.3 Equations of uniformly accelerated motion (SB p. 90) 3. Third equation of motion From the first equation, we have: v 2 = (u + at) 2 = u 2 + 2uat + a 2 t 2 = u 2 + 2a(ut + at 2 /2) v 2 = u 2 + 2as Note: All equations of motion are applicable only if an object moves with uniform acceleration. Go to Example 3 Example 3

6 © Manhattan Press (H.K.) Ltd. End

7 © Manhattan Press (H.K.) Ltd. 2.3 Equations of uniformly accelerated motion (SB p. 89) Uniformly accelerated motion If a body moves with a constant acceleration along a straight line, it is said to have a uniformly accelerated motion. Return to Text

8 © Manhattan Press (H.K.) Ltd. 2.3 Equations of uniformly accelerated motion (SB p. 89) 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. Return to Text

9 © Manhattan Press (H.K.) Ltd. 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. 2.3 Equations of uniformly accelerated motion (SB p. 90)

10 © Manhattan Press (H.K.) Ltd. 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 2.3 Equations of uniformly accelerated motion (SB p. 90)

11 © Manhattan Press (H.K.) Ltd. 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 = v 2 − u 2 v 2 = u 2 + 2as ∴ v = 2.3 Equations of uniformly accelerated motion (SB p. 91)

12 © Manhattan Press (H.K.) Ltd. Solution (cont’d): (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) = s (iii) Error = which is not significant. The test confirms this time. 2.3 Equations of uniformly accelerated motion (SB p. 91) Return to Text