Question

A car accelerates uniformly from rest to speed 6.6 m/s in 6.5 s .Find the distance the car travel during this time .​

Answer 1

The distance the car traveled is 21.45 m

Step-by-step explanation:

Motion With Constant Acceleration

It occurs when an object changes its velocity at the same rate thus the acceleration is constant.

The relation between the initial and final speeds is:

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

Where:

a = acceleration

vo = initial speed

vf = final speed

t = time

The distance traveled by the object is given by:

`\displaystyle x=v_o.t+(a.t^2)/(2)\qquad\qquad [2]`

Solving [1] for a:

`\displaystyle a=(v_f-v_o)/(t)`

Substituting the given data vo=0, vf=6.6 m/s, t=6.5 s:

`\displaystyle a=(6.6-0)/(6.5)`

`a = 1.015\ m/s^2`

The distance is now calculated with [2]:

`\displaystyle x=0*6.5+(1.015*6.5^2)/(2)`

x = 21.45 m

The distance the car traveled is 21.45 m