DP IB Maths: AA SL

Topic Questions

5.6 Kinematics

1a
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2 marks

A skydiver jumps from a moving aircraft at a point directly above a fixed point, O, on the ground.  The trajectory of the skydiver is then modelled by the function

h left parenthesis x right parenthesis equals 3200 minus 0.5 x squared

where h space straight m is the height of the skydiver above the ground and x space straight m is the horizontal distance along the ground from point O.

(i)
Explain the significance of the value 3200 in the model.

(ii)
Calculate the horizontal distance the skydiver covered upon landing.
1b
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2 marks

Sketch a graph of h against x.

1c
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1 mark

Explain why the model is not suitable for values of x larger than 80 space mm.

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2a
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2 marks

A particle moves along a horizontal line starting at the point O. The displacement-time graph for the first 20 seconds of its motion is shown below. Displacement is measured in metres.

q2a-5-6-medium-ib-aa-sl-maths

(i)
Write down the displacement of the particle after 2 seconds.

(ii)
Write down the displacement of the particle after 4 seconds.
2b
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1 mark

Find the velocity of the particle between 13 and 20 seconds.

2c
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1 mark

Find the speed of the particle between 7 and 10 seconds.

2d
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2 marks

Find the total distance travelled by the particle after 20 seconds.

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3a
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2 marks

A cricket ball is projected directly upwards from ground level. The motion of the cricket ball is modelled by the function

h left parenthesis t right parenthesis equals 13 t minus 4.9 t squared space space space space space space space space space space space space t greater than 0

where h metres is the height of the cricket ball above ground level after t seconds.

Find the times at which the cricket ball is exactly 3 m above the ground.

3b
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1 mark

For how long is the cricket ball at least 3 m above the ground?

3c
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2 marks

A player catches the cricket ball (on its way down) at a height of 0.8 m above the ground.

Find the length of time the ball was in the air.

3d
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2 marks

Find the total distance travelled by the ball.

3e
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2 marks

Find the velocity of the cricket ball at t equals 1 second.

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4a
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1 mark

A soft ball is thrown upwards from the top of a 10 m tall building.
The height, h m of the ball above the ground after t seconds is modelled by the function

h left parenthesis t right parenthesis equals H plus 7.8 t minus 4.9 t squared space space space space space space space space space t greater than 0

Write down the value of H.

4b
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2 marks

Find the height of the ball after 2 seconds.

4c
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2 marks

Find the time at which the ball is at the same height as it was when thrown.

4d
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2 marks

Find the time the ball first hits the ground.

4e
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3 marks

Find h apostrophe apostrophe left parenthesis t right parenthesis and hence show that the acceleration at any time is negative 9.8 space straight m divided by straight s squared.

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5a
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2 marks

A particle moves along a straight line with a velocity, v space ms to the power of negative 1 end exponent comma given by v equals 2 to the power of t minus 2  where is t measured in seconds such that 0 less or equal than t less or equal than 4.

Find the acceleration of the particle at time t equals 2 .

5b
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1 mark

State the time when the particle comes to rest.

5c
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3 marks

Find the total distance travelled by the particle.

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6a
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4 marks

A particle is found to have an acceleration, a space ms to the power of negative 2 end exponent, according to the function

a equals 1 over t squared plus sin space t comma  where  t greater or equal than 1

Find an expression for the velocity, v, of the particle given that v left parenthesis 1 right parenthesis equals 1 .

6b
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2 marks

Find the velocity of the particle at space t equals 2 .

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7a
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2 marks

A particle, moving in a straight line, is found to have a velocity space v equals sin space t plus cos space 2 t spacewhere v is measured in ms to the power of negative 1 end exponent and time t is measured in seconds such that 0 less or equal than t less or equal than 5.

Find the time(s) when the particle is instantaneously at rest.

7b
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1 mark

Find the time(s) when the particle changes direction.

7c
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3 marks

Find the distance travelled in the first second of motion.

7d
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3 marks

Find the acceleration of the particle at the instant it first changes direction.

7e
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4 marks

Find the displacement of the particle from its starting point to the point when space t equals 5.

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