Question Bank • QB_FP_ADV_079 NAT • 2 Marks

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Tractor clutches and brakes

Question Statement:

A farm tractor travels at a road transport speed of $v = 36\text{ km/h}$. When the operator suddenly encounters an obstacle, the driver's perception-reaction time is $t_r = 0.75\text{ s}$. The wheel brakes are locked, developing an average braking deceleration of $a = 5.0\text{ m/s}^2$ on a dry tarmac surface. The total stopping distance of the tractor from the moment the hazard is spotted in $\text{m}$ is ________ (round off to 1 decimal place).

Answer Key:

17.5

Step-by-Step Solution & Explanation

``` Tractor Stopping Distance Breakdown: 1. Perception-reaction distance: d_r = v * t_r 2. Braking skid distance: d_b = v^2 / (2 * a) Total Stopping Distance S = d_r + d_b ``` **Step-by-step Calculation:** 1. Initial speed in $\text{m/s}$: $v = \frac{36 \times 1000}{3600} = 10.0\text{ m/s}$ 2. Distance traveled during reaction time $t_r = 0.75\text{ s}$: $d_r = v \times t_r = 10.0\text{ m/s} \times 0.75\text{ s} = 7.50\text{ m}$ 3. Actual braking distance under deceleration $a = 5.0\text{ m/s}^2$: $d_b = \frac{v^2}{2a} = \frac{(10.0)^2}{2 \times 5.0} = \frac{100}{10.0} = 10.0\text{ m}$ 4. Total stopping distance ($S$): $S = d_r + d_b = 7.50 + 10.0 = 17.50\text{ m}$
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