Question

A body with initial velocity 8.0 m/s moves along a straight line with constant acceleration and travels

Answer 1

Answer:

(a) The average velocity is 16 m/s

(b) The acceleration is 0.4 m/s^2

(c) The final velocity is 24 m/s

Explanation:

Constant Acceleration Motion

It's a type of motion in which the velocity (or the speed) of an object changes by an equal amount in every equal period of time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, final speed is calculated as follows:

$v_f=v_o+at\qquad\qquad [1]$

The distance traveled by the object is given by:

$\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2]$

(a) The average velocity is defined as the total distance traveled divided by the time taken to travel that distance.

We know the distance is x=640 m and the time taken t= 40 s, thus:

$\displaystyle \bar v=\frac{x}{t}=\frac{640}{40}=16$

The average velocity is 16 m/s

Using the equation [1] we can solve for a:

$\displaystyle a=\frac{v_f-v_o}{t}$

(c) From [2] we can solve for a:

$\displaystyle a= 2\frac{x-v_ot}{t^2}$

Since vo=8 m/s, x=640 m, t=40 s:

$\displaystyle a= 2\frac{640-8\cdot 40}{40^2}=0.4$

The acceleration is 0.4 m/s^2

(b) The final velocity is calculated by [1]:

$v_f=8+0.4\cdot 40$

$v_f=8+16=24$

The final velocity is 24 m/s