Problem from Mastering Physics

[Raimuna]

I really don't know how to find the acceleration at the intersection.
You are driving to the grocery store at 19 m/s. You are 140 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.77 s and that your car brakes with constant acceleration.
I have found that d1=130m
I tried to find the acceleration and I got 25, but it's wrong.
Could someone help me with this problem?

 

[xcvxcvvc]

you say d1 = 130m Is d1 supposed to be the total distance during the deacceleration(i.e. the initial distance subtracted by how much your car travels during your reaction time)?

if so, how does 140 - 19 * .77 = 130?

As for solving a, use the "big 5"

1/2 a t^2 = d

v=a*t +v(initial)

the above equation can be used to solve a & t. two equations, two unknowns. notice, in the second equation v is zero when your car is completely stopped, the point in time we're interested in.

 

[tomcue]

Based on the information provided, it seems like you are trying to solve for the acceleration of your car as it brakes to a stop at the intersection. To do this, you will need to use the kinematic equations, specifically the one that relates displacement, initial velocity, final velocity, and acceleration (d = (vf^2 - vi^2)/2a).

First, let's determine the final velocity (vf) at the intersection. We know that your initial velocity (vi) is 19 m/s, and your reaction time (t) is 0.77 s. Using the equation vf = vi + at, we can calculate that your final velocity at the intersection is 19 + a(0.77) m/s.

Next, let's use the given information that you are 140 m from the intersection when the light turns red to determine the displacement (d) at the intersection. We know that your initial displacement (d1) is 130 m, so the remaining displacement at the intersection is 140 - 130 = 10 m.

Now, we can plug in the values we have into the kinematic equation: 10 = ((19 + a(0.77))^2 - 19^2)/2a. Solving for a, we get a = -4.62 m/s^2.

This negative value for acceleration indicates that your car is slowing down as it approaches the intersection, which makes sense since you are applying the brakes. It is possible that your answer of 25 was incorrect because you may have accidentally used the reaction time as the total time it takes for your car to come to a stop, instead of just the time it takes for you to react and start braking.

I hope this helps you understand how to solve this problem. Remember to always double check your units and make sure they are consistent throughout your calculations. Good luck!