Question 78: Motion in 1D

Question

An automobile, travelling at $$40\,$$ km/h, can be stopped at a distance of $$40\,$$ m by applying brakes. If the same automobile is travelling at $$80\,$$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :

Accepted Answer

An automobile traveling at 40 km/h can be stopped within a distance of 40 meters by using brakes. If the same automobile is traveling at 80 km/h, we need to determine the minimum stopping distance in meters, assuming no skidding occurs.
First Case
Initial speed, $ u_1 = 40 \, 	ext{km/h} $
Final speed, $ v_1 = 0 \, 	ext{m/s} $
Stopping distance, $ s_1 = 40 \, 	ext{m} $
Using the equation:
$ v^2 - u^2 = 2as $
For the first case:
$ 0^2 - 40^2 = 2a 	imes 40 $
$ -1600 = 80a $
$ a = -20 \, 	ext{m/s}^2 $
Second Case
Initial speed, $ u_2 = 80 \, 	ext{km/h} $
Final speed, $ v_2 = 0 \, 	ext{m/s} $
Similarly, using the same equation:
$ 0^2 - 80^2 = 2a s_2 $
$ -6400 = 2a s_2 $
Since $ a = -20 \, 	ext{m/s}^2 $, divide both sides of the equation for the second case by the first case:
$ \frac{s_2}{40} = \frac{80^2}{40^2} $
$ s_2 = \frac{80 	imes 80}{40} $
$ s_2 = 160 \, 	ext{m} $
Thus, the minimum stopping distance when the automobile is traveling at 80 km/h is 160 meters.

Answer

$$45\,$$ m

Answer

$$100\,$$ m

Answer

$$150\,$$ m

Answer

$$160\,$$ m

Motion in 1D

An automobile, travelling at $40\, km/h, can be stopped at a distance of 40\, m by applying brakes. If the same automobile is travelling at 80\,$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :

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