Question

Receiving two negative values of T in suvat problem when I shouldn't be.

Problem is: A ball is accelerating at a constant rate of 2.54 m*s^-2. After traveling 850 meters it is going at a velocity of 78.19 m*s^-2. How long has the ball been traveling?

My solution: s = vt -1/2at^2 ⇔ 1/2 at^2 -vt +s = 0⇔ t=-v-(v^2 - 2as)/a or -v +(v^2 - 2as)/a

t =(-78.19 - sqrt(78.19^2 -2*2.54*850))/2.54) or (-78.19 + sqrt(78.19^2 -2*2.54*850))/2.54)

from there I get -47.467 or -14.100

Neither of these make sense to me within the context of the problem

Answer 1

In this case, we can write

$2as=v^2-{v_0}^2 (1)$

where v₀ is the initial velocity

In our case, a=2.54 m/s2, s=850 m, v=78.19 m/s

Using (1) we got

V₀=42.37 m/s

The acceleration is given by formula

$a=\frac {v-v_0}{t} (2)$

Using (2) we got

t=14.1 s

Answer

14.1 s