A car traveling 85 km/h strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80 m. What was the average acceleration of the driver during the collision?

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Answer 1 · 2018-02-16T15:53:42

The acceleration is $= - 348.4 m s^{- 2}$ $=-348.4ms^-2$

The initial velocity of the car (driver) is $u = 85 k m h^{- 1}$ $u=85kmh^-1$

$u = \frac{85}{3.6} = 23.61 m s^{- 1}$ $u=85/3.6=23.61ms^-1$

The distance travelled by the driver is $s = 0.80 m$ $s=0.80m$

The final velocity of the driver is $v = 0 m s^{- 1}$ $v=0ms^-1$

Apply the equation of motion,

$v^{2} = u^{2} + 2 a s$ $v^2=u^2+2as$

The acceleration is

$a = \frac{v^{2} - u^{2}}{2 s} = \frac{0 - {23.61}^{2}}{2 \cdot 0.80}$ $a=(v^2-u^2)/(2s)=(0-23.61^2)/(2*0.80)$

$= - 348.4 m s^{- 2}$ $=-348.4ms^-2$