The position of an object moving along a line is given by #p(t) = 2t - 2tsin(( pi )/4t) + 2 #. What is the speed of the object at #t = 7 #?
We're asked to find the speed of an object with a known position equation (one-dimensional).
To do this, we need to find the velocity of the object as a function of time, by differentiating the position equation:
The speed at
The speed of the object is the magnitude (absolute value) of this, which is
The negative sign on the velocity indicates that the particle is traveling in the negative