tuittor.com 1. Teaching Video Additional Mathematics GCE O Level A. Symbols used in Kinematics B. Displacement
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1 1. Teaching Video A. Symbols used in Kinematics s, v, a, B. Displacement Displacement of a particle is measured from its origin to where it is. (a) No Turning t 0s t 2s If ( ) is the displacement function describing the displacement of the particle from the origin, then Distance Travelled Distance Travelled (b) With Turning t 0s t 3s t 2s If ( ) is the displacement function describing the displacement of the particle from the origin, then Distance Travelled Distance Travelled Common Phrase Meaning t s after passing through O Returning to its origin at s Maximum displacement Minimum displacement
2 C. Velocity Common Phrase Initial velocity Instantaneously at rest Maximum velocity Minimum velocity Meaning If a particle turns in its travel,, the sign of velocity after the particle turns, the displacement of the particle after it turns D. Acceleration
3 2. Practice Video A Pause the video (when you are instructed to) in order to give yourself time to practice on each question. Then, play it to check your answer. 1. A particle starts from O and moves in a straight line so that its distance, s cm, from O after time t seconds is given by 20. Calculate its velocity and acceleration when A particle moves in a straight line and its distance, s cm, from a fixed point O, t seconds after passing O, is given by 2. Calculate ( i ) the acceleration of the particle when it comes to an instantaneous rest, (ii ) the velocity of the particle when it is next at O. 3. A particle moves in a straight line so that its distance, s metres, from a fixed point O on the line, is given by ( 3), where t is the time in seconds after passing O. Calculate ( i ) the velocity of P after 2 seconds, (ii ) the values of t when P is instantaneously at rest, (iii) the acceleration of P after 4 seconds. 4. A particle moves in a straight line so that its distance, s metres, from a fixed point after t seconds is given by where d and k are constants. Denoting its velocity by v m/s and its acceleration by a m/s 2, show that. 5. A particle moves in straight line through O so that time t seconds, its distance s metres from O is given by Calculate the distances from O at which the velocity of the particle is zero. Calculate also the accelerations of the particle at the instants when its velocity is zero.
4 3. Practice Video B Pause the video (when you are instructed to) in order to give yourself time to practice on each question. Then, play it to check your answer. 1. A particle moves in a straight line, so that seconds after leaving a fixed point, its displacement, m, is given by 2 4. Given that the particle returns to when, find the value of. ( ) Find the maximum displacement from of the particle during the interval 0. (ii ) Find the total distance travelled by the particle in the period from 0 to A particle moves in a straight line and its distance cm from a fixed point is given by 9 2, where is the time in seconds after passing. Calculate (a) the distance of the particle from when it is instantaneously at rest, (b) its velocity and acceleration when it passes. 3. A particle moves along a straight line so that after seconds its displacement, m, from a fixed point is given by. Calculate ( i ) the value of when is instantaneously at rest, (ii ) the distance travelled by in the first 6 seconds. 4. A particle travels in a straight line through a fixed point. Its distance, m, from is given by 3 ( 4) where is the time in seconds after passing. Calculate (a) the acceleration of when it is instantaneously at rest, (b) the velocity of when it is next at O, (c) the distance travelled by in the 4 th second. 5. A particle moves in a straight line so that its displacement, m, from a fixed point is given by 2 5 2, where is the time in seconds after motion has begun. Calculate the values of at which the particle passes through again.
5 4. Practice Video C 1. A particle moves along a straight line so that at time, where 0, its displacement m from a fixed point is given by 24 ( ). Find (a) the initial distance of from, (b) the acceleration of when it is furthest away from, (c) the speed of when its acceleration is zero. 2. A particle moves in a straight line so that at time seconds, its displacement m from a fixed point, is given by 5 2. ( i ) Find the speed of the particle when 5. (ii ) Find the value(s) of when the particle is instantaneously at rest. (iii) Calculate the average speed of the particle for the first 5 seconds. (iv) Sketch the velocity-time curve for 0, indicating the coordinates of the points of intersection with the axes. 3. A particle moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v m/s, is given by Find ( i ) the values of t for which the particle is at instantaneous rest, (ii ) the acceleration of the particle when the velocity is equal to its initial velocity, (iii) The average speed of the particle during the first four seconds after passing O. 4. A particle moves in a straight line so that, at time t s after leaving a fixed point O, its displacement from O is s m and its velocity is, v m/s. Given that 2, where 0, find ( i ) the value of s when 5, (ii ) an expression for in terms of t, (iii) The value of t for which A particle moves in a straight line so that, t s after leaving a fixed point O, its displacement, s m, is given by 2 3. Given that the particle returns to O when, find the value of T. Using this value of T, find ( i ) the maximum displacement from O of the particle during the interval 0, (ii ) the acceleration of the particle at time T s.
6 5. Practice Video D Pause the video (when you are instructed to) in order to give yourself time to practice on each question. Then, play it to check your answer. 1. A particle P moves in a straight line so that its displacement, s m, from a fixed point O is given by 4 3, where t is the time in seconds measured from the start of the motion. Calculate (a) the velocity of P at 3, (b) the value of s at the instant when P reverses its direction of motion, (c) the acceleration of then particle when Particles P and Q move in the same straight line so that their distances in metres from a fixed point O on the line are given by 4 2 and ( 2) respectively, where t is the time measured in seconds after P passes through A and Q passes through B. (A and B are points on the line). Assuming that after P and Q meet, they move continuously without stopping, find (a) The values of t when P and Q meet, (b) The distance travelled by P when they meet the second time. 3. A body moves in a straight line from a fixed point O. Its distance from O, s metres, is given by, where t is the time in seconds after passing through O. Find (a) The time when the body returns to O, (b) The velocity at this instant, (c) The value of t when the body is instantaneously at rest, (d) The distance moved by the body in the 2 nd second. 4. A particle moves in a straight line so that its displacement from a fixed point O, t seconds after leaving O, is given by 4 2 8, where s is in centimetres. Find (a) the velocity and acceleration of the particle in terms of t, (b) the time when the particle first comes to instantaneous rest, (c) the velocity of the particle when 3, (d) the maximum velocity of the particle. 5. A particle P moves in a straight line and displacement s cm from a fixed point O after t seconds is given by 6 2. Find (a) the values of t when the magnitude of the acceleration is 1 cm/s 2, (b) the value of t when the particle returns to O, (c) the maximum displacement from O, (d) the total distance travelled during the first 3 seconds.
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