Question

A UFO experienced a constant acceleration for 97 s during which its displacement was 56,454 m north and was going 1164 m/s north at the end of said acceleration. Determine the magnitude of the UFO's acceleration & the initial speed of the UFO. a = Vi =

Answer 1

Time taken

26 = 1

Displacement

d=56454 m

Final velocity

Using the following kinematics equation

$v_f=v_i+at$

at = 1 - ) 습

Using the following kinematics equation

$d=v_it+\frac12at^2$

Using (1)

$d=v_it+\frac t2(v_f-v_i)$

$d=v_it+\frac {v_ft}2-\frac {v_it}2$

$d=\frac {v_it}2+\frac {v_ft}2$

$\frac {v_it}2=d-\frac {v_ft}2$

$v_i=\frac{2d}{t}-v_f$

Substituting values

$v_i=\frac{2\times56454\ m}{97\ s}-1164\ m/s$

$\boxed{v_i=0\ m/s}$

Substituting into (1)

$at=v_f-v_i$

$a=\frac{v_f-v_i}{t}$

$a=\frac{1164\ m/s-0}{97\ s}$

$\boxed{a=12\ m/s^2}$