Question

A car traveling 54.8 km/h is 23.3 m from a barrier when the driver slams on the brakes. The car hits the barrier 1.84 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact?

Answer 1

Given, u = 54.8 km/h = 54800/3600 = 15.22 m/s

S = 23.3 m , t = 1.84 s

(a) let 'a' be the constant deceleration.

Applying,

S= ut - ½at²

Or, 23.3 = 15.22 × 1.84 - ½× a × 1.84²

Or, 23.3 = 28.0048 - 1.6928 × a

Or , a = (28.0048 - 23.3) / 1.6928

Or, a= 2.78 m/s² (ans)

(b) let 'v' be the final velocity before impact.

Applying

v² = u² - 2× a × s

Or, v² = 15.22² - 2× 2.78 × 23.3 = 102.1004

Or, v = √102.1004

Or, v = 10.104 m/s (ans)

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