A car moving at a constant rate decelerates and comes to a halt over a distance of 125m. If the car decelerates at 1.5m/s^2, how long does it take the car to stop?

I'm thinking I should use the equation: V final^2 = V intitial*t + 1/2at^2 But my acceleration is negative and I can't take the square root of a negative.

Question

A car moving at a constant rate decelerates and comes to a halt over a distance of 125m. If the car decelerates at 1.5m/s^2, how long does it take the car to stop?

I'm thinking I should use the equation: V final^2 = V intitial*t + 1/2at^2 But my acceleration is negative and I can't take the square root of a negative.

anonymous · Answer

The equation you present is not valid. The right side has units of distance while the left side has units of velocity^2.

Having said that, you know $$v_f=0$$$$\Delta d = 125 \text{ m}$$$$a=-1.5 \frac{ \text{m} }{ \text{s}^2 }$$and you are looking for $ \Delta t$.

Consider using$$v_f^2 = v_i^2 + 2a \Delta d$$to find $v_i$, and then use$$v_f = v_i + 2a \Delta t$$to find $\Delta t$.

anonymous · Answer

Sorry. The second equation should read$$v_f = v_i + a \Delta t$$