A driver is moving at 17.0 m/s when she sees a child on a bike 65m ahead of her. If the car can brake at 4.9 m/s2 and the drivers reaction time is 1.6 s, can she avoid hitting the child

First, find the distance she travels before reacting:

Δx = v₀ t + ½ at²

Δx = (17.0 m/s) (1.6 s) + ½ (0 m/s²) (1.6 s) ²

Δx = 27.2 m

Now find the distance she travels before stopping:

v² = v₀² + 2aΔx

(0 m/s) ² = (17.0 m/s) ² + 2 (-4.9 m/s²) Δx

Δx = 29.5 m

The total distance traveled is:

27.2 m + 29.5 m = 56.7 m

56.7 m is less than 65 m, so yes, she can avoid hitting the child.