Answer to Question #208505 in Classical Mechanics for dave

Question

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. Calculate the acceleration of the object.

Answer 1

$x(t) = v_0t +\frac{at^2}{2}$

$v_0 =0$

$x(t) = \frac{at^2}{2}$

$x(1) = \frac{a}{2}$

$x(2) = 2a$

$x(2)-x(1)=12$

$x(2)-x(1)=2a-\frac{a}{2}=\frac{3a}{2}$

$\frac{3a}{2}=12$

$a=8$

$\text{Answer: }8 \ \frac{m}{s^2}$