Question

a truck accelerates uniformly at the rate of 1.2 m/s^2 for a distance of 50 m. If the truck started with an initial velocity of 3 m/s, wht is its velocity at the end of 50m?

Answer 1

Recall that

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

where
`v_i`,
`v_f` are the truck's initial and final velocities, respectively;
`a` is its acceleration; and
`\Delta x` is the total change in its position. We have everything we need in order to solve for
`v_f`. Note that the truck's acceleration is always positive, so we should expect the final velocity to also be positive.

`{v_f}^2-\left(3\,(\mathrm m)/(\mathrm s)\right)^2=2\left(1.2\,(\mathrm m)/(\mathrm s^2)\right)(50\,\mathrm m)`

`\implies{v_f}^2=129\,(\mathrm m^2)/(\mathrm s^2)`

`\implies v_f=11.4\,(\mathrm m)/(\mathrm s)`