At the end of a delivery ramp, a skid pad exerts a constant force on a package so that the package comes to rest in a distance d. The ramp is changed so that the same package arrives at the skid pad at a higher speed and the stopping distance is 2d.
A) What happens to the time interval required for the package to stop?

increases by a factor of

Explanation:

First we need to find the initial velocity for it to stop at the distance 2d using the following equation of motion:

where v = 0 m/s is the final velocity of the package when it stops, is the initial velocity of the package when it, a is the deceleration, and is the distance traveled.

So the equation above can be simplified and plug in Δs = d, for the 1st case

(1)

For the 2nd scenario where the ramp is changed and distance becomes 2d,

(2)

let equation (2) divided by (1) we have:

So the initial speed increases by . If the deceleration a stays the same and time is the ratio of speed over acceleration a

The time would increase by a factor of

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