AP CALC BC
Last of the “new” material that isn’t really new except for notation.
Vector functions in the xy-plane. Given F (t )  x(t ), y (t )  or F (t )  x(t ) i + y (t ) j, we can merely treat the
vector function the same way as we did parametric functions. All the same formulas and methods apply.
For each of the following functions:
(a) Rewrite in parametric form
(b) Sketch the curve, indicating direction
(c) Compute the velocity and acceleration vectors
(d) Evaluate the velocity vector at t = 1 and draw that particular
vector on the graph in a contrasting color.
(e) Find an expression for the speed of a particle traveling along
the curve.
(f) Find the length of the curve
dy
d2y
(g) Compute
and
dx
dx 2
(h) Determine where, if anywhere, the slope of the curve is zero or undefined.
(i) Determine the intervals for t where the curve is concave up.
1. (to be done together as a class) F (t )  e t  e t ,5  2t  for  1  t  2
2. F (t )  t  t 2 , 43 t 3 / 2  for 0  t  2
3. F (t )  1  e t , t 2  for  3  t  3
AP CALC BC
Last of the “new” material that isn’t really new except for notation.
Vector functions in the xy-plane. Given F (t )  x(t ), y (t )  or F (t )  x(t ) i + y (t ) j, we can merely treat the
vector function the same way as we did parametric functions. All the same formulas and methods apply.
For each of the following functions:
(a) Rewrite in parametric form
(b) Sketch the curve, indicating direction
(c) Compute the velocity and acceleration vectors
(d) Evaluate the velocity vector at t = 1 and draw that particular
vector on the graph in a contrasting color.
(e) Find an expression for the speed of a particle traveling along
the curve.
(f) Find the length of the curve
dy
d2y
(g) Compute
and
dx
dx 2
(h) Determine where, if anywhere, the slope of the curve is zero or undefined.
(i) Determine the intervals for t where the curve is concave up.
1. (to be done together as a class) F (t )  e t  e t ,5  2t  for  1  t  2
2. F (t )  t  t 2 , 43 t 3 / 2  for 0  t  2
3. F (t )  1  e t , t 2  for  3  t  3