Question

1. You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is negligible and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Answer 1

Answer:

-1.82m/s²

Explanation:

Given that the reaction time (t) is negligible and car brakes with constant acceleration.

Initial Velocity (u) = 20m/s

Distance(d) from Intersection when light turns red = 110m

Hence, the magnitude of braking acceleration that will bring the car to rest at exactly the intersection :

Using the motion equation:

v² = u² + 2as

Where v = final velocity at the intersection

u = initial velocity ; s = distance to intersection ; a = acceleration of the car

Exactly at the intersection ; v = 0

0 = 20² + 2×a×110

0 = 400 + 220a

-400= 220a

a = - 400 / 220

a = - 1.818

a = - 1.82 m/s²

- stands for negative acceleration (deceleration)