Question

A un objeto se le aplicó una aceleración de 8m/s durante 20 seg .Si se sabe que en ese periodo recorrió 100m ¿cuál es la velocidad inicial y final del objeto?

Answer 1

Answer: v0 = -75m/s, vf = 85m/s

Step-by-step explanation:

This question can be transslated to:

An object is accelerated with 8m/s^2 during 20 seconds. In that time the object travel a distance of 100m. Which is the initial and final speed of the object?

We know that the acceleration is:

a(t) = 8m/s^2

for the speed, we integrate over time:

v(t) = (8m/s^2)*t + v0, where v0 is the initial speed, on of the things we are looking for.

For the position we integrate again, and let's use that the initial position is equal to zero, because we only know that in the period of 20 seconds the object displaced a distance of 100m.

p(t) = (8m/s^2)*(1/2)*t^2 + v0*t

now, we know that p(20s) = 100m, with this we can find the value of v0

100m = (4m/s^2)*(20s)^2 + v0*20s = 1600m + v0*t

100m - 1600m = -1500m = v0*20s

v0 = -1500m/20s = -75m/s

now, with the initial velocity, we can imput it in the equation for the velocity and get:

v(t) = (8m/s^2)*t -75m/s

for the final velocity, we evaluate this equation in t = 20s

v(20s) = (8m/s^2)*20s - 75m/s = 85m/s

(we evaluate in 20s because after this time the object is not longer accelerated, this means that the velocity will not change anymore)