Question

A car was moving with a velocity 24ms-1
. Suddenly the driver saw a child on his way, just 8m away from
the car. The driver immediately pressed the brakes. But it was too late; the car skidded to a halt at 12m.
What was the velocity of the car at the moment when it ran over the child?

Answer 1

Answer on Question #50142, Physics, Mechanics | Kinematics | Dynamics

A car was moving with a velocity $24\,\mathrm{ms}^{-1}$. Suddenly the driver saw a child on his way, just $8\,\mathrm{m}$ away from the car. The driver immediately pressed the brakes. But it was too late; the car skidded to a halt at $12\,\mathrm{m}$. What was the velocity of the car at the moment when it ran over the child?

Solution:

**Kinematics equation**

$$2ad = -v_i^2$$

where $a$ is acceleration, $d = 12\,\mathrm{m}$ is distance to stop, $v_i$ is initial velocity.

Thus,

$$a = \frac{-v_i^2}{2d} = \frac{-24^2}{2 \cdot 12} = -24\,\mathrm{m/s^2}$$

**Again kinematics equation**

$$a = \frac{v_f^2 - v_i^2}{2d_2}$$ $$v_f = \sqrt{v_i^2 + 2ad_2} = \sqrt{24^2 - 2 \cdot 24 \cdot 8} = 8\sqrt{3} = 13.86\,\mathrm{m/s}$$

**Answer:** $v_f = 13.86\,\mathrm{m/s}$

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