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

$v_f=v_0+at\implies v_f=0\,\dfrac{\mathrm m}{\mathrm s}+\left(6.00\,\dfrac{\mathrm m}{\mathrm s^2}\right)(4.10\,\mathrm s)$

$\implies v_f=24.6\,\dfrac{\mathrm m}{\mathrm s}$

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

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

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