Question 1.9: An object moves along a straight line so that its position a...

An Introduction to Mathematics for Engineers: Mechanics

An object moves along a straight line so that its position at time t in seconds is given by

x = 2t³ – 6t (in metres) (t ≥ 0) .

i) Find expressions for the velocity and acceleration of the object at time t.
ii) Find the values of x, v and a when t = 0, 1, 2 and 3.
iii) Sketch the graphs of x, v and a against time.
iv) Describe the motion of the object.

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i) Position x = 2t³ – 6t ①

Velocity v = $\frac{dx}{dt}$ = 6t² – 6 ②

Acceleration a = $\frac{dv}{dt}$ = 12t ③

You can now use these three equations to solve problems a bout the motion of the object.

ii) when	t=	0	1	2	3
from ①	x=	0	-4	4	36
from ②	v=	-6	0	18	48
from ③	a=	0	12	24	36

iii) The graphs are drawn under each other so that you can see how they relate.

fig 1.39

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