An object with initial velocity of 20 m/s accelerates uniformly at 5 m/s in the direction of its motion for a distance of 10 m. What is the final velocity of the object?

Answer 1

a = 5
v = 5t + c
when t = 0, v = 20
20 = 0+c ---> c = 20

then
v = 5t + 20

when s is the distance,
s = (5/2)t^2 + 20t + k
when t = 0, s = 0
0 = 0 + 0 + k ---> k = 0

s = (5/2)t^2 + 20t

how long did it take to go 10 m ?
10 = (5/2)t^2 + 20t
20 = 5t^2 + 40t
t^2 + 8t = 5
I will complete the square, which is the easiest way for this equation
t^2 + 8t + 16 = 5 + 16
(t+4)^2 = 21
t+4 = √21
t = √21-4 seconds

for that value of t,
v = 5(√21 - 4) + 20 m/s or appr 22.9 m/s

Answer 2

120M