Question

The distance required for a car to come to a stop will vary depending on how fast the car is moving. Suppose that a certain car traveling down the road at a speed of 10 m/s can come to a complete stop within a distance of 20 m . Assuming the road conditions remain the same, what would be the stopping distance required for the same car if it were moving at speeds of 5 m/s, 20 m/s, or 40 m/s ?

Answer 1

Answer:

when speed becomes v = 5 m/s

$d_1 = \frac{20}{4} = 5 m$

when speed = 20 m/s

$d_2 = 4(20) = 80 m$

when speed = 40 m/s

$d_2 = 16(20) = 320 m$

Explanation:

Initial speed of the car is given as

$v_i = 10 m/s$

now we have

stopping distance = 20 m

final speed = 0

now we have

$v_f^2 - v_i^2 = 2 a d$

now we have

$0 - 10^2 = 2(a)(20)$

$a = -\frac{100}{40} = -2.5 m/s^2$

now we know that

all conditions remains the same

so stopping distance depends on the speed as

$d = \frac{v^2}{2a}$

now when speed becomes v = 5 m/s

so it is half of the above speed

so the stopping distance becomes 1/4 times

$d_1 = \frac{20}{4} = 5 m$

when speed = 20 m/s that is double the given speed

then the stopping distance becomes 4 times

$d_2 = 4(20) = 80 m$

when speed = 40 m/s that is four times the given speed

then the stopping distance becomes 16 times

$d_2 = 16(20) = 320 m$

Answer 2

The stopping distance required for the same car at speeds of 5 m/s, 20 m/s, or 40 m/s is 5m, 80m, and 320 m.

What would be the stopping distance required for the same car if it were moving at speeds of 5 m/s, 20 m/s, or 40 m/s?

We know that according to the third equation of motion,

$v^2 - u^2 = 2as$

given to us

speed of the car, u = 10 m/s

Distance, s = 20 m

Substitute the value to find the deceleration,

$v^2 - u^2 = 2as\\\\0^2 - 10^2 = 2(a)(20)\\\\-100 = 40a\\\\a = -2.5\ m/s^2$

The stopping distance required for the same car,

A.) speed, u = 5 m/s

$v^2 - u^2 = 2as\\\\0^2 - 5^2 = 2(-2.5)s\\\\s = 5\ m$

B.) speed, u = 20 m/s

$v^2 - u^2 = 2as\\\\0^2 - 20^2 = 2(-2.5)s\\\\s = 80\ m$

C.) speed, u = 40 m/s

$v^2 - u^2 = 2as\\\\0^2 - 40^2 = 2(-2.5)s\\\\s = 320\ m$

Hence, the stopping distance required for the same car at speeds of 5 m/s, 20 m/s, or 40 m/s is 5m, 80m, and 320 m.

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