AP Calc 7.10: AP Calculus Exam Questions: Motion

AP Calc AB 1969 #35:  No Calculator

At t = 0 a particle starts at rest and moves along a line in such a way that at time t its acceleration is  $24t^2$ feet per second per second.  Through how many feet does the particle move during the first 2 seconds?

• (A)  32

• (B)  48

• (C)  64

• (D)  96

• (E)  192

AP Calc AB 1985 #14: No Calculator

The velocity of a particle moving on a line at time t is
 $v\ =\ 3t^{\frac{1}{2}}+5t^{\frac{3}{2}}$  meters per second.  How many meters did the particle travel from t = 0 to t = 4?

• (A)  32

• (B)  40

• (C)  64

• (D)  80

• (E)  184

AP Calc AB 1973 #8: No Calculator

A particle moves in a straight line with velocity  $v\left(t\right)\ =\ t^2$ .  How far does the particle move between times t = 1 and t = 2?

• (A)  $\frac{1}{3}$  

• (B) $\frac{7}{3}$  

• (C)  3

• (D)  7

• (E)  8

AP Calc AB 1973 #13: No Calculator

The acceleration a of a body moving in a straight line is given in terms of time t by  $a=8-6t$ .  If the velocity of the body is 25 at t = 1 and if s(t) is the distance of the body from the origin at time t, what is s(4) - s(2)?

• (A)  20

• (B)  24

• (C)  28

• (D)  32

• (E)  42

AP Calc AB 1993 #11: No Calculator

The acceleration of a particle moving along the x-axis at time t is given by  $a\left(t\right)\ =\ 6t\ -\ 2$ .  If the velocity is 25 when t= 3 and the position is 10 when t = 1, then the position x(t) = 

• (A)   $9t^2+1$  

• (B)   $3t^2-2t+4$  

• (C)   $t^3-t^2+4t+6$  

•  (D)   $t^3-t^2+9t-20$  

• (E)   $36t^3-4t^2-77t+55$