The position of an object moving along a line is given by $p(t) = t - tsin(( pi )/3t)$ . What is the speed of the object at $t = 1$ ?

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Answer 1 · 2017-04-28T22:26:41

$p'(1) ~~ -0.389$ distance units/time units

The speed of the object at any given time, $t_1$ , is the first derivative, $p'(t)$ , evaluated that time.

Compute the first derivative:

$p'(t) = 1 - sin(pi/3t)-pi/3tcos(pi/3t)$ distance units/time units

Evaluate at t = 1:

$p'(1) ~~ -0.389$ distance units/time units

The position of an object moving along a line is given by p(t) = t - tsin(( pi )/3t) p(t) = t - tsin(( pi )/3t) . What is the speed of the object at t = 1 t = 1 ?