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Constant Acceleration

Change in velocity = Final velocity - Initial velocity. Acceleration = Change in Velocity. Time. a = (v - u). t. Constant Acceleration.

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Constant Acceleration

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  1. Change in velocity = Final velocity - Initial velocity Acceleration = Change in Velocity Time a = (v - u) t Constant Acceleration Acceleration is how quickly the velocity is changing - the change in velocity per unit time. If the acceleration is constant, this can then be expressed as the following equation: Where: a is acceleration v is the final velocity u is the initial velocity t is time taken

  2. From... a = (v - u) t v = u + at Constant Acceleration We rearrange the formula to make v the subject... at = v - u (multiply both sides by t) at + u = v (add u to both sides) Rewriting, gives...

  3. Calculating the Distance Travelled Consider an object accelerating from an initial velocity u to a final velocity v in t seconds... As before, to calculate the distance travelled, we need to find the area underneath the graph...

  4. s = ut + ½ at2 Area ofLilacRectangle Area ofBlueTriangle From: = Base x Height = t x u = ut = ½ Base x Height = ½ x t x (v - u) = ½ x t x (at) a = (v - u) t at = v - u = ½ at2 Calculating the Distance Travelled Total Area = ut + ½ at2 so theformula for distance travelled (s), is…

  5. s = (u + v) x t Average speed = Total distance travelled 2 Total time taken u + v = s 2 t Average Speed We also know that the average speed can be calculated from... If we multiply both sides of the equation by t we can find out s... This formula allows us to calculate the distance travelled if we know the initial and final velocities and the time taken.

  6. s = (u + v) x t 2 We can combine formulas and by eliminating t... The first step is to make t the subject of formula s = ut + ½ at2 v = u + at v - u = t a t = v - u a Constant Acceleration Formulas We now have 3 constant acceleration formulas… v = u + at v - u = at (subtracting u from both sides) (dividing both sides by a) (rewriting)

  7. The second step is to substitute this value for t into formula s = (u + v) x t 2 s = (u + v) x (v - u) 2 a t = v - u a So the fourth constant acceleration formula is: v2 = u2 + 2as Constant Acceleration Formulas Multiply both sides by 2a... 2as = (u + v) (v - u) Multiply out the brackets... 2as = v2 - u2 Add u2 to both sides and rewrite... v2 = u2 + 2as

  8. Constant Acceleration Formulas - Summary We now have 4 formulas. These formulas will help you calculate any motion problem in which a body undergoes zero or constant acceleration. Whenever you have any 3 of the five ‘v-u-s-t-a’ unknowns, you can find out the remaining 2 unknown values by using one or more of the above formulas…

  9. s = (u + v ) x t 2 Using Constant Acceleration Formulas s = ut + ½at2 v = u + at v2 = u2 + 2as

  10. Projectile Motion - Forces Acting Ignoring airresistance, the only force acting on a projectile during the flight is gravity. Projectiles have a downwardacceleration (due to gravity) and this only affects the verticalvelocity. For a projectile there is noacceleration in the horizontaldirection. Horizontal Vertical

  11. Altering Projectile Velocity A cannon ball is fired horizontally at a target. Can you find out (or calculate) the correct velocity to hit the target?

  12. Calculating Time Taken Example: Calculate the time taken, from firing, for the cannon ball to hit the target. t = d/s is a formula that can be applied to solve problems, whenever velocity is constant... Velocity is constant in the horizontal vector... t = d/s t = 48/24 t = 2 Time taken is 2s

  13. Calculating Final Velocity v = u + at is a formula that can be applied to solve problems, whenever acceleration is constant... Example: Calculate the final vertical velocity of the cannon ball as it hits the target. In this case a = g = 9.8ms-2 (9.8m/s2) v = u + at v = 0 + 9.8 x 2 v = 0 + 19.6 v = 19.6m/s Final vertical velocity is 19.6m/s

  14. Kinetic Energy • 2 starting equations • Force = m x a (Newton’s 2nd law) • W = Force x distance • Together give • Work = (m x a) x distance • W = m x a x d

  15. Work is MAD • Av Speed (velocity) is distance time • Distance = Average velocity x time • Distance = v + u x t 2

  16. Distance • Distance = v + u x t 2 • D = ½ x v + u x t • Starting velocity is zero • D = ½ x v x t

  17. Time • Final velocity = acceleration x time • Time = final velocity acceleration • t = v a

  18. Going back a step….. • D = ½ x v x t • D = ½ x v x v a • D = ½ x v2 a

  19. Put into previous statements • W = m x a x d • W = m x a x ½ x v2 a • W = m x ½ x v2 • W = ½ x m x v2

  20. GPE • work done = Force x distance • Force = mass x acceleration • Gravitational constant (g) is the cause of the acceleration • Force = mass x gravitational constant • F = m x g • Work = mass x acceleration x distance • In this case height is the distance therefore, PE=mgh

  21. Work • Work = force x distance • Measured in Joules. • Weight is a force, mass is not

  22. Power • Power = work / time (s) • Measured in Joules/second or Watts

  23. Newton’s 2nd law • Force = mass x acceleration • Force in Newton’s • Mass in kg • Acceleration in m/s2

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