Question

Kinetic equation problem

Answer 1

Use the kinematic formula

`{v_2}^2 - {v_1}^2 = 2a\Delta x`

where
`v_1,v_2` are initial/final velocities,
`a` is acceleration, and
`\Delta x` is displacement. We're given
`a=-5.00(\rm m)/(\rm s^2)` and
`\Delta x=15.0\,\rm m`, and the car comes to a stop so
`v_2=0`. Solve for
`v_1`.

`-{v_1}^2 = 2\left(-5.00(\rm m)/(\rm s^2)\right) (15.0\,\mathrm m) \\\\ ~~~~ \implies {v_1}^2 = 150.(\rm m^2)/(\rm s^2) \\\\ ~~~~ \implies v_1 = \sqrt{150.(\rm m^2)/(\rm s^2)} \approx \boxed{12.2 (\rm m)/(\rm s)}`