Annie comes to a sudden stop to avoid hitting a deer crossing the road at night. As she hits the breaks, her speed drops from 12 m/s to zero in 1.5 seconds. How far did she travel during that time?

Answer 1

As Annie hits the brakes the car's speed which was initially 12 m/s, slows to 0 m/s.

This takes place within 1.5 s. So the change in velocity (-12 m/s) per unit time is equal to (-12/1.5 m/s²), which is acceleration. Acceleration = -8 m/s² (which is deceleration).

Using the equation of motion for a body with an initial position (x₀) and velocity (v₀) undergoing constant acceleration (a) we have:

x = x₀ + (v₀)(t) + (a)(t)²

Assume x₀ = 0 because we don't know where we are on the road.

Initial speed, v₀, is given as 12 m/s.

Acceleration is -8 m/s².

The stop occurs in 1.5 seconds, so t=1.5 s.

Substituting gives:

x = (12 m/s)(1.5 s) + (-8 m/s²)(1.5 s)²

x = 18 m - (8 m/s²)(2.25 s²)

x = 18 m - 9 m

x = 9 m