Question

Problem 1 You and your family are going to Graceland, via interstate. After a stop in San Diego, you begin accelerating uniformly from rest along an entrance ramp. At 7s into this acceleration, your little brother hits the start button on a stopwatch he is playing with. When the stopwatch reads 3s, you enter the freeway and begin cruising at a constant 100Km kim (a)What is your acceleration along the ramp, in meters per second per second (SI units)? (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?

Answer 1

Initial velocity,$u=0m/s$

total time taken for acceleration ,$t=10s$

final velocity ,$v=100km/hr=27.78m/s$

(a)

Use Formula $v=u+at$

$27.78m/s=0m/s+a*10s$

$27.78=0+10a$

ANSWER: ${\color{Red} a=2.778m/s^{2}}$

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(b)

Use Formula $s=ut+1/2at^{2}$

$s=0m/s*10s+0.5*2.778m/s^{2}(10s)^{2}$

$s=0*10+0.5*2.778*10^{2}$

ANSWER: ${\color{Red} s=138.9m}$

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(c)

Use Formula $v=u+at$

$v_{7}=0m/s+2.778m/s^{2}*{\color{Blue} 7s}$

ANSWER: ${\color{Red} v_{7}=19.446m/s=70km/hr}$

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(d)

Use Formula $s=ut+1/2at^{2}$

$s_{7}=0m/s*10s+0.5*2.778m/s^{2}(7s)^{2}$

$s_{7}=0*10+0.5*2.778*7^{2}$

ANSWER: ${\color{Red} s_{7}=68.06m}$

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