Question

Your car can brake with a deceleration of 6 m/s2. The car is initially going at 40 m/s.
a) How long will it take the car to come to a full stop?

b) If the car is 5 meters long, about how many car lengths should be kept between you and the car in front of you (assume the car in front of you comes to a stop immediately).

Answer 1

The time of motion of the car before coming to a full stop is 6.67 s.

The car length that should be kept between you and the car is 138.33 m.

The given parameters;

• acceleration of the car, a = - 6m/s²
• initial velocity of the car, u = 40 m/s

The time of motion of the car before coming to a full stop is calculated as follows;

$v = u + at\\\\when \ the \ car \ stops , \ v = 0\\\\0 = u + at\\\\0 = 40 -6t\\\\6t = 40\\\\t = \frac{40}{6} = 6.67 \ s$

The distance traveled by the car before coming to a full stop;

$v^2 = u^2 + 2as\\\\0 = u^2 + 2as\\\\0 = 40^2 -2(6)s\\\\0 = 40^2- 12s\\\\12s = 1600\\\\s = \frac{1600}{12} \\\\s = 133.33 \ m$

The car length that should be kept between you and the car is calculated as;

car length in front of you = 5 m + 133.33 m = 138.33 m

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