Answer:
The acceleration of the object during the motion is 1.6 m/s²
Explanation:
Lets explain how to solve the problem
An object moving on the x-axis with a constant acceleration
Its distance increases 80 meter in 5 seconds
Its final velocity is 20 m/s
We need to find the acceleration of the object during this motion
To solve the problem we will use two equations:
First: [tex]s=ut+\frac{1}{2}at^{2}[/tex], where s is the displacement, u is the
initial velocity, t is the time, and a is the acceleration
Second: v = u + at, where v is the final velocity
s = 80 , t = 5 , v = 20 we have two missing a and u, so we will use the
system of equations to find them
Substitute s, t in the first equation
[tex]80=u(5)+\frac{1}{2}a(5)^{2}[/tex]
80 = 5u + 12.5a
5u + 12.5a = 80 ⇒ (1)
Substitute V and t in the second equation
20 = u + a(5)
20 = u + 5a
u + 5a = 20 ⇒ (2)
Lets solve equations (1) and (2)
Multiply equation (2) by -5 to eliminate u
-5u - 25 a = -100 ⇒ (3)
Add equations (1) and (3)
-12.5 a = -20
Divide both sides by -12.5
a = 1.6
The acceleration of the object during the motion is 1.6 m/s²
