Question

A truck moving at 5 m/s is about to accelarate at the rate of 2 m/s in 3s.after 3s the driver saw a old lady about to cross the road and it took 0.8 sec before it hits the brake. If the maximum braking deceleration is 5m/s2 and its distance of the truck to the old lady is 50m. Does the old lady hit by the truck?

Answer 1

Answer on Question #47855, Physics, Computational Physics

A truck moving at $5\mathrm{m/s}$ is about to accelerate at the rate of $2\mathrm{m/s}$ in 3s. After 3s the driver saw an old lady about to cross the road and it took 0.8 sec before it hits the brake. If the maximum braking deceleration is $5\mathrm{m/s}^2$ and its distance of the truck to the old lady is $50\mathrm{m}$. Does the old lady hit by the truck?

Solution:

Given:

$$\begin{array}{l} v_{1} = 5 \mathrm{m/s}, \\ a_{1} = 2 \mathrm{m/s}^{2}, \\ t_{1} = 3 \mathrm{s}, \\ t_{2} = 0.8 \mathrm{s}, \\ a_{2} = -5 \mathrm{m/s}^{2}, \\ D = 50 \mathrm{m}, \\ \end{array}$$

The kinematic equation that describes an object's motion is:

v2 = v1 + a1 * t1
v2 = 5 + 2 * 3
v2 = 11 m/s

The distance covered before driver hits the brake

d1 = v2 * t2
d1 = 11 * 0.8
d1 = 8.8 m

The kinematic equation that describes braking deceleration:

d2 = (v_f**2 - v2**2) / (2 * a2)
d2 = (0 - 11**2) / (-2 * 5)
d2 = 12.1 m

Thus, before stop truck covered distance

$$\begin{array}{l} d = d_{1} + d_{2} = 8.8 + 12.1 = 20.9 \mathrm{m} \\ d < 50 \mathrm{m} \\ \end{array}$$

**Answer**: Truck does not hit the old lady.

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