Adriver notices an upcoming speed limit change from 45 mi/h (20 m/s) to 25 mi/h (11 m/s). if she estimates
the speed limit will change in 50 m, what acceleration is needed to reach the new speed limit before it begins?

Explanation:

Given that,

Initial speed of the vehicle, u = 45 mi/h = 20 m/s

The final speed of the vehicle, v = 25 mi/h = 11 m/s

The speed limit will change in 50 m i.e. the distance is, d = 50 m

To find,

The acceleration of the vehicle that is needed to reach the new speed limit before it begins.

Solution,

Let a is the acceleration of the vehicle. It can be calculated using third equation of motion i.e.

Solving for a.

Put all the values,

The acceleration of the vehicle is and it is deaccelerating.

Reference:

link

-2.79 m/s²

Explanation:

Given:

v₀ = 20 m/s

v = 11 m/s

Δx = 50 m

Find: a

v² = v₀² + 2aΔx

(11 m/s)² = (20 m/s)² + 2a (50 m)

a = -2.79 m/s²

Round as needed.