Question

A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance?

• A. 4 m
• B. 6 m
• C. 8 m
• D. 2 m

Hint:

From motion's third equation, we get \(v^2 - u^2 = 2as\).

Answer 1

The Correct Option is C

To solve this problem, we will use the concept of stopping distance in motion, which is defined by the formula:

S = \frac{v^2}{2a}

where:

• S is the stopping distance.
• v is the initial speed.
• a is the deceleration.

Initially, the car is moving at 40 km/h and stops in 2 meters. First, we need to convert the speed into meters per second:

40 \text{ km/h} = \frac{40 \times 1000}{3600} \text{ m/s} \approx 11.11 \text{ m/s}

Using the stopping distance formula, we have:

2 = \frac{(11.11)^2}{2a}

Solving for a:

a = \frac{(11.11)^2}{4} \approx 30.86 \text{ m/s}^2

Now, we calculate the stopping distance for a speed of 80 km/h:

80 \text{ km/h} = \frac{80 \times 1000}{3600} \text{ m/s} \approx 22.22 \text{ m/s}

Substitute v = 22.22 \text{ m/s} and a = 30.86 \text{ m/s}^2 into the stopping distance formula:

S = \frac{(22.22)^2}{2 \times 30.86}

Calculating the above expression gives:

S \approx 8 \text{ meters}

Therefore, the minimum stopping distance when the car is moving at 80 km/h is 8 meters.