You and your family are traveling via interstate to Foreman, AR in a vintage aut

Question

You and your family are traveling via interstate to Foreman, AR in a vintage automobile. After a stop in Fort Smith, you begin accelerating uniformly from rest along an entrance ramp. At 11s into this acceleration, your little brother hits the start button on a stopwatch he is playing with. When the stopwatch reads 6s, you are entering the freeway and begin cruising at a constant 65mph.

(a) What is your acceleration along the ramp in mi hr2 ?

(b) How long is the ramp?

(c) How fast were you going when your brother hit the start button on his stopwatch?

(d) How far along the ramp were you when your brother hit the start button?

Explanation / Answer

Initial speed u = 0 mph

final speed v = 65 mph

We use the formula:

v = u +at

Time elapsed: 11 + 6 seconds = 17 seconds = 17/(60*60) =17/3600 hr

65 = 0 + a * 17/3600

a * 17/3600 = 65

or,

1. a = 65 * 3600/17 = 13764 miles /h2

2. Length of ramp: s:

We use:

v2 - u2 = 2as

652 = 2 * 13764 *s

or,

s = 4225/(2*13764) = 0.153 miles

3. speed when t = 11 s = 11/3600 hr

we use: v' = u + at' = 0 + 13764 * 11/ 3600 = 42.1 mph

4. distance covered on ramp till t = 11 seconds:

v2 - u2 = 2as

42.12 = 2 * 13764 *s

or,

s = 1772.4/(2* 13764 ) = 0.064 miles

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