AH 1.1 Kinematic Relationships Flashcards

The linear equations of motion - their derivations and applications.

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1
Q

Derive the kinematic relationship v=u+at

A
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2
Q

Derive the kinematic relationship

s = ut + 1/2 at2

A
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3
Q

Derive the kinematic relationship v2 = u2 + 2as

A
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4
Q

A body undergoes uniform acceleration.

Write down the general equation for its displacement s with respect to time t.

A

s = ut + ½ at2

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5
Q

The initial velocity of a body is 20 ms-1 and it’s acceleration is 6 ms-2.

Write down the particular equation for the displacement of this body.

A

s = 20t + 3t2

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6
Q

A body has diplacement equation s = 20t + 3t2

Using differentiation, find the equation for the velocity of this body.

Show all reasoning.

A

v = ds/dt

= d/dt (20t + 3t2)

v = 20 + 6t

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7
Q

Given the velocity equation for a moving body is v = 20 + 6t, differentiate this velocity equation to confirm that the acceleration is 6 ms-2. Show all steps of reasoning.

A

a = dv/dt

= d/dt (20 + 6t)

a = 6 ms-2

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8
Q

The displacement of a firework rocket for the first 3 seconds of its motion is given by the equation

s = 8t3 + 4t2

Find expressions for the velocity and acceleration of the rocket. Show all steps of reasoning.

A

v = ds/dt

v = 24t2 + 8t

a = dv/dt

a = 48t +8

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9
Q

The displacement of a firework rocket is given by s = 8t3 +4t2

After 3 seconds find the displacement of the rocket.

A

s = 252 m

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10
Q

The velocity of a firework rocket is given by

v = 24t2 + 8t

Find the velocity after 3 seconds.

A

v = 240 ms-1

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11
Q

The acceleration of a firework rocket is given by the equation a = 48t +8

Findf the acceleration after 3 seconds.

A

a = 152 ms-2

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12
Q

Give a physical reason for why the displacement, velocity and acceleration equations for a firework rocket after launch only hold for the first 3 seconds.

A

The firework rocket must have run out of fuel after 3 seconds.

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13
Q

The displacement of a firework rocket after launch is given by s = 8t3 +4t2

Give a mathematical reason why this equation only holds for 3 seconds.

A

The displacement equation suggests that s increases indefinitely!

This is clearly impossible as there is only a finite amount of fuel.

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