Answer to Question #104565 in Mechanics | Relativity for Prince

Question

An object has a constant acceleration a=4m/s². It's velocity is 1m/s at t=0, when it is at x=7m. How fast is it moving when it is at x=8m? At what time is this?

Answer 1

$a=4\ m/s^2$

$v_i=1\ m/s, \ \ x_i=7\ m$ , $t=0 \ s$

$v_f \ - ?, \ x_f=8\ m$ , $t - ?$

Solution:

Using formula $v_f^2=v_i^2 +2ad, (d$ - displacement$)$ we have:

$v_f^2=1^2+2\times 4\times (8-7)=9, \; \; v_f=3\ m/s$

To find time (when $v_f=3\ m/s$ ) we can use formula for velocity of object with constant acceleration:

$v_f=v_i+at,$

$t=\frac{v_f-v_i}{a}=\frac{3-1}{4}=0.5 \ s$

Answer: $v_f=3 \ m/s, \; t=0.5\ s.$