Date | May 2017 | Marks available | 2 | Reference code | 17M.2.AHL.TZ1.H_11 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Calculate | Question number | H_11 | Adapted from | N/A |
Question
Xavier, the parachutist, jumps out of a plane at a height of metres above the ground. After free falling for 10 seconds his parachute opens. His velocity, , seconds after jumping from the plane, can be modelled by the function
His velocity when he reaches the ground is .
Find his velocity when .
Calculate the vertical distance Xavier travelled in the first 10 seconds.
Determine the value of .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
(M1)
A1
[2 marks]
(M1)
A1
[2 marks]
(M1)
A1
(M1)(A1)
A1
[5 marks]
Examiners report
Syllabus sections
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18M.2.SL.TZ2.S_9a:
Find the initial velocity of P.
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18M.2.SL.TZ2.S_9d:
Find the acceleration of P when it changes direction.
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19M.1.SL.TZ1.S_7b:
Find the total distance travelled in the first 5 seconds.
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19M.2.SL.TZ2.S_8c:
Find the value of when particle A first changes direction.
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22M.2.SL.TZ1.5b:
Find the acceleration of the particle when it changes direction.
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21N.1.SL.TZ0.7b:
Sketch a graph of against , clearly showing any points of intersection with the axes.
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18M.2.SL.TZ1.S_10a:
Find the coordinates of A.
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18M.2.SL.TZ1.S_10b.i:
For the graph of , write down the amplitude.
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18M.2.AHL.TZ2.H_7b.ii:
Find the value of the acceleration of P at time t1.
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16N.2.SL.TZ0.S_9b:
Find the value of .
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17M.2.SL.TZ1.S_7a.i:
Write down the first value of at which P changes direction.
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17M.2.SL.TZ1.S_7a.ii:
Find the total distance travelled by P, for .
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17M.2.AHL.TZ1.H_11c:
Determine the value of .
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17N.2.SL.TZ0.S_9b:
Hence or otherwise, find all possible values of for which the velocity of P is decreasing.
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18M.2.SL.TZ2.S_9e:
Find the total distance travelled by P.
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SPM.2.SL.TZ0.6a:
Find the maximum distance of the particle from O.
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19N.2.SL.TZ0.S_10c:
During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.
Find the total time taken for the two stages.
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18M.2.SL.TZ1.S_10e:
Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
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18M.3.AHL.TZ0.Hca_4a:
Show that .
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19N.2.AHL.TZ0.H_9b.i:
the value of .
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19M.2.SL.TZ2.S_8d:
Find the total distance travelled by particle A in the first 3 seconds.
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18N.2.SL.TZ0.S_4a:
Find when the particle is at rest.
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16N.2.SL.TZ0.S_9a:
Find the initial velocity of .
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18M.2.AHL.TZ2.H_7b.i:
Find an expression for the acceleration of P at time t.
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SPM.2.SL.TZ0.6b:
Find the acceleration of the particle at the instant it first changes direction.
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18M.2.SL.TZ1.S_10d:
Find the maximum speed of the ball.
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18M.3.AHL.TZ0.Hca_4c:
Hence show that the Maclaurin series for up to and including the term in is .
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18M.2.SL.TZ2.S_9b:
Find the maximum speed of P.
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18M.2.AHL.TZ2.H_7a:
Determine the first time t1 at which P has zero velocity.
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18M.3.AHL.TZ0.Hca_4b:
By differentiating the above equation twice, show that
where and denote the 3rd and 4th derivative of respectively.
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16N.2.SL.TZ0.S_9c:
(i) Find the value of .
(ii) Hence, find the speed of P when .
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19N.2.AHL.TZ0.H_9a.ii:
Hence, write down the maximum speed of the body.
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18M.3.AHL.TZ0.Hca_4d:
Use this series approximation for with to find an approximate value for .
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17N.1.AHL.TZ0.H_5:
A particle moves in a straight line such that at time seconds , its velocity , in , is given by . Find the exact distance travelled by the particle in the first half-second.
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19M.2.SL.TZ2.S_8e.i:
Given that particles A and B start at the same point, find the displacement function for particle B.
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17M.1.AHL.TZ2.H_4b:
Find the displacement of the particle when
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22M.2.SL.TZ1.5c:
Find the total distance travelled by the particle.
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19N.2.AHL.TZ0.H_9b.ii:
the distance travelled between and .
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EXN.2.SL.TZ0.3a:
Find the value of .
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20N.2.AHL.TZ0.H_11e.i:
Show that, at these times, .
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20N.2.AHL.TZ0.H_11c:
Find the maximum displacement of , in metres, from its initial position.
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19N.2.AHL.TZ0.H_9a.i:
Determine the coordinates of point and the coordinates of point .
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17N.2.SL.TZ0.S_9a:
Write down the values of when .
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17M.2.AHL.TZ1.H_11a:
Find his velocity when .
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21M.2.SL.TZ1.5c:
Find the acceleration of the particle when .
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21M.1.AHL.TZ2.11d:
Deduce a similar expression for in terms of .
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19M.2.SL.TZ2.S_8a:
Find the initial displacement of particle A from point P.
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20N.2.AHL.TZ0.H_11b:
Find an expression for in terms of .
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20N.1.SL.TZ0.S_7b:
Particle also moves in a straight line. The position of is given by .
The speed of is greater than the speed of when .
Find the value of .
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18M.2.SL.TZ1.S_10b.ii:
For the graph of , write down the period.
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19M.2.SL.TZ2.S_8e.ii:
Find the other value of when particles A and B meet.
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17M.1.AHL.TZ2.H_4a:
Find and .
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21M.1.AHL.TZ2.11a:
By solving an appropriate differential equation, show that the particle’s velocity at time is given by .
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21M.1.SL.TZ2.9b.i:
Find the value of .
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18M.2.SL.TZ2.S_9c:
Write down the number of times that the acceleration of P is 0 m s−2 .
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19N.2.AHL.TZ0.H_9b.iii:
the acceleration when .
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21M.1.AHL.TZ2.11c:
By using the result to part (b) (i), show that .
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17N.2.SL.TZ0.S_9d:
Find the total distance travelled by P when its velocity is increasing.
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18N.2.SL.TZ0.S_4b:
Find the acceleration of the particle when .
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21M.1.AHL.TZ2.11b.ii:
By solving an appropriate differential equation and using the result from part (b) (i), find an expression for in terms of .
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19N.2.SL.TZ0.S_10b:
Find the distance that the rocket travels during the first stage.
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19N.2.AHL.TZ0.H_9c:
Find the distance travelled in the first 30 seconds.
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EXN.2.SL.TZ0.3b:
Let be the distance travelled by the particle from to and let be the distance travelled by the particle from to .
Show that .
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21M.1.SL.TZ2.9b.ii:
Find the displacement of particle A from the origin when .
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21M.1.SL.TZ2.9d:
Find the value of .
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21M.1.AHL.TZ2.11e:
Hence, show that .
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21N.1.SL.TZ0.7c:
Find the total distance travelled by .
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21N.1.SL.TZ0.7a.ii:
Show that the distance of from at this time is metres.
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22M.2.SL.TZ1.5a:
Find the value of when the particle is at rest.
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22M.2.SL.TZ2.6a:
Determine when the particle changes its direction of motion.
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19M.2.SL.TZ2.S_8b:
Find the value of when particle A first reaches point P.
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17N.2.SL.TZ0.S_9c:
Find an expression for the velocity of P at time .
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18M.2.SL.TZ1.S_10c:
Hence, write in the form .
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19N.2.SL.TZ0.S_10a:
Find an expression for the velocity, m s−1, of the rocket during the first stage.
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17M.2.SL.TZ2.S_7:
Note: In this question, distance is in metres and time is in seconds.
A particle moves along a horizontal line starting at a fixed point A. The velocity of the particle, at time , is given by , for . The following diagram shows the graph of
There are -intercepts at and .
Find the maximum distance of the particle from A during the time and justify your answer.
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20N.2.AHL.TZ0.H_11a:
Find the times when comes to instantaneous rest.
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20N.2.AHL.TZ0.H_11e.ii:
Hence show that .
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21M.2.SL.TZ1.5b:
Find the total distance travelled by the particle.
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20N.2.AHL.TZ0.H_11d:
Find the total distance travelled by in the first seconds of its motion.
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20N.1.SL.TZ0.S_7a:
Find an expression for the velocity of at time .
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17M.2.SL.TZ1.S_7b:
A second particle Q also moves along a straight line. Its velocity, after seconds is given by for . After seconds Q has travelled the same total distance as P.
Find .
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19M.2.AHL.TZ2.H_6:
A particle moves along a horizontal line such that at time seconds, ≥ 0, its acceleration is given by = 2 − 1. When = 6 , its displacement from a fixed origin O is 18.25 m. When = 15, its displacement from O is 922.75 m. Find an expression for in terms of .
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18N.2.SL.TZ0.S_4c:
Find the total distance travelled by the particle.
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19M.1.SL.TZ1.S_7a:
Find the value of .
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16N.2.SL.TZ0.S_9d:
(i) Find the total distance travelled by P between and .
(ii) Hence or otherwise, find the displacement of P from A when .
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21M.2.SL.TZ1.5a:
Find the smallest value of for which the particle is at rest.
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21M.1.SL.TZ2.9e:
A second particle, particle B, travels along the same straight line such that its velocity is given by , for .
When , the distance travelled by particle B is equal to .
Find the value of .
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21M.1.SL.TZ2.9a:
Find the value of .
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21M.1.SL.TZ2.9c:
Find the distance of particle A from the origin when .
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21M.1.AHL.TZ2.11b.i:
Show that the time taken for the particle to reach satisfies the equation .
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21N.1.SL.TZ0.7a.i:
Find the value of when reaches its maximum velocity.