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Kinematics: The relationship between Distance, Speed & Acceleration

Calculus HOME | Achievement Objectives | Gradient | Gradient Functions | Differentiation | Gradient at a point | Find point with gradient | Equation of Tangent | Second Derivitive | Coordinates of Max & Min | Increasing, Decreasing Functions | Applications | Kinematics with differentiation | Antidifferentiation | Finding 'C' | Kinematics with anti-differentiation | Rates of Change | Mixed Problems | Revision

13

Kinematics using Differentiation

What is distance, velocity, acceleration?

Differentiate a distance function to get speed (velocity) function

Differentiate a velocity function to get acceleration function

Linking distance, speed, and acceleration functions using differentiation and introduce anti-differentiation

Class Notes | Blank Notes

Ex17.02

NuLake p98

Bouncing ball & speed graph (java applet)

Leaning tower of pizza (java applet)

Rollercoaster: slow to load but well worth the wait

 Moving man java (great)

Projectile rocket | gravity

Mouse over below

Distance function S=

Speed function V=

Acceleration Function  A=

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Find the speed of a car at t = 4 seconds, given the distance (metres) is defined by
d = t2 - 6t + 15

Steps:

d = t2 - 6t +15

1) Differentiate to find 'speed' function

v = 2t - 6

2) Substitute t = 4 into the 'speed' function

v = 2t - 6
v = 2x4 - 6
v = 8 - 6

3) Speed at t = 4 sec

v = 2 m/s

 

Find the acceleration of a car at t = 2 seconds, given the distance (metres) is defined by
d = t2 - 6t + 15

Steps:

d = t2 - 6t +15

1) Differentiate to find 'speed' function

v = 2t - 6

2) Differentiate again to find the 'acceleration' function

a = 2

3) Substitute t = 4 into the 'acceleration' function

Note: nowhere to substitue in t = 4 (acceleration here is always 2)

4) Acceleration at t = 4 sec

a = 2 m/s/s

 

Find the acceleration of a car at t = 2 seconds, given the distance (m) is defined by d = 3t3 - 9t2 + 18

Steps:

d = 3t3 - 9t2 + 18

1) Differentiate to find 'speed' function

v = 9t2 - 18t

2) Differentiate again to find the 'acceleration' function

a = 18t - 18

3) Substitute t = 2 into the 'acceleration' function

a = 18t - 18
a = 18x2 - 18
a = 18 m/s/s

Class Notes | Blank Notes Screen Snaps

 

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