Question

a race car accelerates uniformly from 18.5 m/s to 46.1m/s in 2.47 seconds detrrmine the acceleration of the car and distance traveled

Answer 1

Because acceleration is constant, the acceleration of the car at any time is the same as its average acceleration over the duration. So

`a=(\Delta v)/(\Delta t)=(46.1\,(\mathrm m)/(\mathrm s)-18.5\,(\mathrm m)/(\mathrm s))/(2.47\,\mathrm s)=11.2\,(\mathrm m)/(\mathrm s^2)`

Now, we have that

`{v_f}^2-{v_0}^2=2a\Delta x`

so we end up with a distance traveled of

`\left(46.1\,(\mathrm m)/(\mathrm s)\right)^2-\left(18.5\,(\mathrm m)/(\mathrm s)\right)^2=2\left(11.2\,(\mathrm m)/(\mathrm s^2)\right)\Delta x`

`\implies\Delta x=79.6\,\mathrm m`