Question

A Roller coaster car is moving 19.8 m/s on flat ground when it hits the brakes. It decelerates at -3.77 m/s squared over the next 45.8 m how much time does it take? Please help me. I have been trying for the past hour

Answer 1

Answer:

12.5s

Explanation:

The equation for the position for a uniform acceleration is:

$x=\frac{1}{2}at^2+v_0t+x_0$

x position

a acceleration

t time

v₀ initial velocity

x₀ initial position

The given equation has only one unknown. Solve for time t:

$\frac{a}{2}t^2+v_0t + x_0-x=0\\t^2+\frac{2v_0}{a}t+\frac{2(x_0-x)}{a}=0\\t_{1/2}=-\frac{v_0}{a}^+_-\sqrt{(\frac{v_0}{a})^2-\frac{2(x_0-x)}{a}}$