The position of an object moving along a line is given by $p(t) = t - tsin(( pi )/4t)$ . What is the speed of the object at $t = 1$ ?

Question

1352 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-03T13:25:41

The speed is $=-0.33ms^-1$

The speed is the derivative of the position.

$p(t)=t-tsin(pi/4t)$

$v(t)=p'(t)=1-sin(pi/4t)-pi/4tcos(pi/4t)$

When $t=1$

$v(1)=1-sin(pi/4)-pi/4cos(pi/4)$

$=1-sqrt2/2-pi/4*sqrt2/2$

$=1-0.707-0.555$

$=-0.33$

The position of an object moving along a line is given by p(t) = t - tsin(( pi )/4t) p(t) = t - tsin(( pi )/4t) . What is the speed of the object at t = 1 t = 1 ?