Question

a car travelling with a speed of 60km/hr brakes and comes to rest within a distance of 20m. if the speed of the car were 120km/hr, the stopping distance will be?

Answer 1

Answer on Question 59554, Physics, Mechanics | Relativity

Question:

A car travelling with a speed of $60 \, \text{km/h} \, \text{r}$ brakes and comes to rest within a distance of $20 \, \text{m}$. If the speed of the car were $120 \, \text{km/h} \, \text{r}$, the stopping distance will be?

Solution:

Let's first find the deceleration of the car from the kinematic equation:

$$v _ {f} ^ {2} = v _ {i} ^ {2} + 2 a d,$$

here, $v_{f} = 0 \, ms^{-1}$ is the final speed of the car, $v_{i}$ is the initial speed of the car, $a$ is the deceleration of the car and $d$ is the stopping distance.

Then, from this formula we can find the deceleration of the car:

$$- v _ {i} ^ {2} = 2 a d,$$ $$a = \frac {- v _ {i} ^ {2}}{2 d}.$$

Let's convert the initial speed of the car from $km/h$ to $m/s$:

$$v _ {i} = \left(60 \, \frac {k m}{h r}\right) \cdot \left(\frac {1 0 0 0 \, m}{1 \, k m}\right) \cdot \left(\frac {1 \, h r}{3 6 0 0 \, s}\right) = 1 6. 6 6 \, \frac {m}{s}.$$

Then, we can calculate the deceleration of the car:

$$a = \frac {- v _ {i} ^ {2}}{2 d} = \frac {- \left(1 6 . 6 6 \, \frac {m}{s}\right) ^ {2}}{2 \cdot 2 0 \, m} = - 6. 9 4 \, \frac {m}{s ^ {2}}.$$

As we know the deceleration of the car, we can find the new stopping distance of the car from the same kinematic equation:

$$d _ {n e w} = \frac {- v _ {i n e w} ^ {2}}{2 a}.$$

Let's again convert the new initial speed of the car from $km/h$ to $m/s$:

$$v _ {i n e w} = \left(1 2 0 \, \frac {k m}{h r}\right) \cdot \left(\frac {1 0 0 0 \, m}{1 \, k m}\right) \cdot \left(\frac {1 \, h r}{3 6 0 0 \, s}\right) = 3 3. 3 3 \, \frac {m}{s}.$$

Then, we can calculate the new stopping distance of the car (if the speed of the car were $120 \, \text{km/hr}$):

$$d_{new} = \frac{-v_{inew}^2}{2a} = \frac{-\left(33.33 \, \frac{\text{m}}{\text{s}}\right)^2}{2 \cdot \left(-6.94 \, \frac{\text{m}}{\text{s}^2}\right)} = 80 \, \text{m}.$$

Answer:

$$d_{new} = 80 \, \text{m}.$$

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