An automobile engineer found that the impact of a truck colliding at 16 km/h with a concrete pillar caused the bumper to indent only 6.2 cm. the truck stopped. determine the acceleration of the truck during the collision.

An important assumption to solve this problem is that the acceleration is uniform (constant).

Under that assumption you can use following formulae.

Acceleration = [Final velocity - Initial velocity] / time

You have final velocity = 0 and initial velocity = 16 km/h

Then you need to find the time.

Average velocity = [distance / time]

In this case the distance is the deformation of the bumper: 6.2 cm = 0.062 m = 0.000062 km

And when acceleration is constant, the average speed is equal to [Initial velocity + Final velocity] / 2 = [16 km/h + 0] /2 = 8 km/h

Now you can calculate time solving from Average velocity = [distance / time]

time = distance / average velocity =  0.000062 km / 8 km/h = 0.00000775 h

And, finally we can use the formula Acceleration = [Final velocity - Initial velocity] / time

Acceleration = [16 km/h - 0 km/h] / 0.00000775 h = 2,064,516 km/h^2

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