Question

In 2.0 s, a particle moving with constant acceleration along the x axis goes from x = 10 m to x = 50 m. The velocity at the end of this time interval is 10 m/s. What is the acceleration of the particle?

Answer 1

-10 m/s²

Step-by-step explanation

The displacement of the particle is,

`\Delta x=50m-10m=40m`

We know that the final velocity is 10m/s, after 2 seconds. To find the acceleration, we have to find the initial velocity too.

We know that the displacement is,

`\Delta x=(v_i+v_f)/(2)\cdot t`

Solving for the initial velocity vi,

`v_i=(2\Delta x)/(t)-v_f`

Replace with the values,

`v_i=(2\cdot40m)/(2s)-10m/s=40m/s-10m/s=30m/s`

The final velocity is also a function of the acceleration,

`v_f=v_i+a\cdot t`

Solving for a,

`a=(v_f-v_i)/(t)`

Replace with the values,

`a=(10m/s-30m/s)/(2s)=(-20m/s)/(2s)=-10m/s^2`

Hence, the acceleration of the particle is -10m/s².