Question

A car is traveling at 11.12 m/s and a child runs out in front of the car 33.37 m in front of it. The driver instantly applies the brakes. What acceleration must the car experience in order to avoid the child?

Answer 1

The car must experience an acceleration of 3.49 m/s² to avoid hitting the child.

Step-by-step explanation:

To determine the required acceleration for the car to avoid hitting the child, we employ the kinematic equation v² = u² + 2as, where:

v is the final velocity (0 m/s as the car stops),

u is the initial velocity of the car (11.12 m/s),

a is the acceleration we need to find,

s is the displacement (33.37 m).

Rearranging the equation to solve for acceleration, we use a = (v² - u²) / (2s). Substituting the known values, a = (0 - (11.12)²) / (2 * 33.37), which simplifies to a = -3.49 m/s².

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, aligning with the car's deceleration to stop.

In conclusion, to prevent hitting the child, the car must undergo an acceleration of 3.49 m/s², which acts in the direction opposite to its initial motion, considering the initial velocity and the stopping distance.