Question

Plz. help ) An auto accelerates forward from 7.0 m/s at a uniform

0.71 m/s?. It travels a distance of 1033 m while
accelerating

(a) How fast is the auto moving just as it is traveled
the 1033 m?

(b) How many seconds did it take to travel the 1033 m?​

Answer 1

The auto is moving at 38.9 m/s

The auto took 45 seconds to travel the 1033 m

Step-by-step explanation:

Constant Accelerated Motion

it's a type of motion in which the velocity of an object changes uniformly in time.

The relationship between initial and final speeds is calculated by the equation:

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

Where a is the constant acceleration, vo the initial speed, vf the final speed, and t the time.

Another useful equation allows us to calculate the distance x traveled by the object:

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

(a)

Solving [1] for t and substituting into [2] we find the equation:

`v_f^2=v_o^2+2ax`

This last equation will be used to solve the first part of the problem which gives the initial speed of vo=7 m/s, the uniform acceleration as a=0.71 m/s^2 and the distance traveled as x=1033 m, thus substituting:

`v_f^2=7^2+2(0.71)(1033)`

`v_f^2=49+1466.86=1515.86`

Thus:

`v_f=√(1515.86)=38.9`

`v_f=38.9 m/s`

The auto is moving at 38.9 m/s

(b)

To calculate the time, we solve [1] for t:

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

`\displaystyle t=(38.9-7)/(0.71)=45`

The auto took 45 seconds to travel the 1033 m