The position of an object moving along a line is given by $p(t) = 4t - tsin(( pi )/8t)$ . What is the speed of the object at $t = 3$ ?

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Answer 1 · 2016-06-20T08:28:05

In one dimension, speed is just the magnitude of velocity, such that if we had a negative value we would just take the positive version.

To find the speed function, we will need to differentiate the position function with respect to t:

Let $s(t)$ be the speed function:
$s(t)=4-sin(pi/8t)-pi/8tcos(pi/8t)$
(I've assumed proficiency with the product and chain rule)

Therefore the speed at $t=3$ is given by:
$s(3)=4-sin(3pi/8)-3pi/8cos(3pi/8)$
$s(3)=2.63ms^-1$ (ensuring the take the trig functions in radians)

The position of an object moving along a line is given by p(t) = 4t - tsin(( pi )/8t) p(t) = 4t - tsin(( pi )/8t) . What is the speed of the object at t = 3 t = 3 ?