AP Calculus BC
SVA Problems
Worksheet 2.4a
For the following position functions s of a point moving on a line, find:
a) v(t)
b) a(t)
c) when the particle is to the right or left of the origin
d) when the particle moves left and move right
e) when the particle speeds up and slows down
f) sketch the path of the particle
1. s  t   4t 3  9t 2  6t  2,  3, 3
2. s  t   t 4  4t  1,  3, 3
3. s  t  
t
,  2, 2
t 1
2
4. s  t   t  5  5t  2t 2  , .5, 2.5
5. s  t   2t 3  13t 2  22t  5, 0, 4
6. A dynamite blast propels a heavy rock straight up with a launch velocity of 160 ft/sec (about 109 mph). It
reaches a height of s  160t  16t 2 ft after t seconds.
a) How high does the rock go?
b) What is the velocity and speed of the rock when it is 256 ft above the ground on the way up? on the
way down?
c) What is the acceleration of the rock at any time t during its flight (after the blast)?
d) When does the rock hit the ground? What is the velocity at this time?
7. A spherical balloon is inflated with helium at the rate of 100  ft 3 / min .
a) How fast is the balloon’s radius increasing at the instant the radius is 5 ft?
b) How fast is the surface area increasing at that instant?
8. A man 6 ft tall walks at the rate of 5 ft/sec toward a streetlight that is 16 ft above the ground. At what rate is
the length of his shadow changing when he is 10 ft from the base of the light? At what rate is the tip of his
shadow moving?
9. A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is
being pumped into the tank at a rate of 2 m 3 / min , find the rate at which the water level is rising when the
water is 3 m deep.