Question

high-speed test vehicle is brought to rest by throwing out a drag chute behind it, causing a constant acceleration of −13 m/s2. The vehicle has a velocity of 56 m/s when the chute is deployed. What is the minimum length of track needed for this process?

Answer 1

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Question #46581 – Physics – Mechanics | Kinematics | Dynamics

High-speed test vehicle is brought to rest by throwing out a drag chute behind it, causing a constant acceleration of $-13\ \mathrm{m/s^2}$. The vehicle has a velocity of $56\ \mathrm{m/s}$ when the chute is deployed. What is the minimum length of track needed for this process?

Solution:

The vehicle moves with constant acceleration in a straight line.

Equations of motion:

**Displacement and Acceleration:**

$$d = v_0 t + \frac{\alpha t^2}{2}$$

**Velocity and Acceleration:**

$$v = v_0 + \alpha t$$

**Where:**

$$v_0 = 56\ \mathrm{m/s}$$ $$\alpha = -13\ \mathrm{m/s^2}$$

To find the distance, we find the time which the vehicle was moving.

When the vehicle stops speed becomes equal to 0, so $v = 0$

$$0 = 56 - 13t$$ $$t = \frac{56}{13} \cdot s = 4.31 \cdot s$$ $$d = 56 \cdot 4.31 - \frac{13 \cdot 4.31^2}{2} = 120.6\ \mathrm{m}$$

**Answer:** the minimum track length should be $121\ \mathrm{m}$.