"Caleb misjudges while parking, and bumps his car into a brick wall at 3 MPH. His bumper brings the car to a stop in about 2 inches. We wish to estimate the force the wall exerts on the car during this bump. The force is about:"

Explanation:

Using equation of motion to determine the acceleration of the car,

vf^2 = vi^2 + 2 * a * S,

vf = 0

0 = vi^2 + 2 * a * S

Converting mph to m/s,

3 mph * 5280 ft/mi * 12 in/ft * 2.54 cm/in * 1 m/100 cm * 1 h/3600 s

= 3 * 0.445

v = 1.335 m/s

Converting in to m,

2 in * 2.54 cm/in * 1 m/100 cm = 0.0254 m

= 2 * 0.0254

S = 0.0508 m

0 = 1.335^2 + 2 * a * 0.0508

a = -1.335^2 ÷ 0.1013

= -17.54 m/s^2

Mass of car (assumed) = 2000 kg

Force = ma

= 2000 × 17.54

= 35.08 kN.

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