Question

Object moving on the

x

axis with a constant acceleration increases its

x

coordinate

by 80 m in a time of 5.0 s and has a velocity of +20 m/s at the end of this time.

Determine the acceleration of the object during this motion

​

Answer 1

The acceleration of the object during the motion is 1.6 m/s²

Step-by-step 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:
`s=ut+(1)/(2)at^(2)`, 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

`80=u(5)+(1)/(2)a(5)^(2)`

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