Question

Ben rushin is waiting at a stoplight. when it finally turns green, ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. determine the displacement of ben's car during this time period

Answer 1

In the 4.10 seconds that elapsed, Ben reaches a velocity of

`v_f=v_0+at\implies v_f=0\,(\mathrm m)/(\mathrm s)+\left(6.00\,(\mathrm m)/(\mathrm s^2)\right)(4.10\,\mathrm s)`

`\implies v_f=24.6\,(\mathrm m)/(\mathrm s)`

In this time, his displacement
`\Delta x` satisfies

`{v_f}^2-{v_0}^2=2a\Delta x\implies\left(24.6\,(\mathrm m)/(\mathrm s)\right)^2-\left(0\,(\mathrm m)/(\mathrm s)\right)^2=2\left(6.00\,(\mathrm m)/(\mathrm s^2)\right)\Delta x`

`\implies\Delta x=50.4\,\mathrm m`