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    Equiz #2 (Automotive)

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    1. A police officer chasing a motorist at 34 mph accelerates at 3.0 m/s^2. It takes the officer 10 seconds to catch up, reaching a speed of 30 mph. Each vehicle has traveled 150 meters. 2. A trip normally taking 2 hours and 20 minutes at 105 km/h takes 50 minutes longer at 70 km/h due to heavy traffic. 3. A Honda Civic's velocity is calculated over different time intervals based on its distance traveled as a function of time. Its average velocity is found to be 2.8 m/s from 0-2s, 5.2 m/s from 0-4s, and 7.6 m/s

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    Equiz #2 (Automotive)

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    Secret Secret
    62 views5 pages
    1. A police officer chasing a motorist at 34 mph accelerates at 3.0 m/s^2. It takes the officer 10 seconds to catch up, reaching a speed of 30 mph. Each vehicle has traveled 150 meters. 2. A trip normally taking 2 hours and 20 minutes at 105 km/h takes 50 minutes longer at 70 km/h due to heavy traffic. 3. A Honda Civic's velocity is calculated over different time intervals based on its distance traveled as a function of time. Its average velocity is found to be 2.8 m/s from 0-2s, 5.2 m/s from 0-4s, and 7.6 m/s

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    eQuiz #2 [Automotive]

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    1. A police officer chasing a motorist at 34 mph accelerates at 3.0 m/s^2. It takes the officer 10 seconds to catch up, reaching a speed of 30 mph. Each vehicle has traveled 150 meters. 2. A trip normally taking 2 hours and 20 minutes at 105 km/h takes 50 minutes longer at 70 km/h due to heavy traffic. 3. A Honda Civic's velocity is calculated over different time intervals based on its distance traveled as a function of time. Its average velocity is found to be 2.8 m/s from 0-2s, 5.2 m/s from 0-4s, and 7.6 m/s

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    62 views5 pages

    Equiz #2 (Automotive)

    Uploaded by

    Secret Secret
    1. A police officer chasing a motorist at 34 mph accelerates at 3.0 m/s^2. It takes the officer 10 seconds to catch up, reaching a speed of 30 mph. Each vehicle has traveled 150 meters. 2. A trip normally taking 2 hours and 20 minutes at 105 km/h takes 50 minutes longer at 70 km/h due to heavy traffic. 3. A Honda Civic's velocity is calculated over different time intervals based on its distance traveled as a function of time. Its average velocity is found to be 2.8 m/s from 0-2s, 5.2 m/s from 0-4s, and 7.6 m/s

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 5

    1.

    An SUV travelling with constant velocity of 15 m/s (about 34 mi/h) passes corner of UST
    Espana Blvd and Lacson. As the motorist passes, a PNP officer on his motorcycle stopped at
    the corner starts off in pursuit with constant acceleration of 3.0 m/s².
    a) How much time will elapse before the officer catches up with the motorist?
    b) What is the officer's speed at that point?
    c) What is the total distance each vehicle has traveled at that point?

    m m
    a.) v SUV =15 ;v =0 ; aofficer =3.0
    s 0 officer
    s2

    SSUV =S officer

    1
    SSUV =v SUV t ; S officer =v o t + aofficer t 2
    officer
    2

    1
    v SUV t= aofficer t 2
    2

    2 v SUV
    =t
    aofficer

    m
    2(15
    )
    s
    t=
    m
    3.0 2
    s

    t=10 s

    b.) vf officer
    =v 0 officer
    + aofficer t

    vf officer
    ( ms )(10 s )
    = 3.0 2

    m
    vf =30
    officer
    s

    c.) SSUV =v SUV t

    SSUV = 15 ( ms ) (10 s)
    SSUV =150 m
    SSUV =S officer

    Sofficer =150 m

    2. You normally drive on the expressway between Manila and Tarlac at an average speed of 105
    km/h (65 mi/h) and the trip takes 2 h and 20 mins. On a Friday afternoon, however, heavy
    traffic slows you down and you drive the same distance at an average speed of only 70 km/h
    (43 mi/h). How much longer does the trip take?

    7
    v ave =105 km/h ; t 1=2 h 20 min¿ h
    1
    3

    v ave =70 km/h


    2

    S=v ave t 1=v ave t 2


    1 2

    v ave t 1
    t 2= 1

    v ave 2

    t 2=
    (105 km/h ) ( 73 h)
    70 km/h

    t 2=3.5 h=3 h 30 min

    ∆ t=t 2−t 1

    ∆ t=3 h 30 min−¿ 2 h 20 min¿

    ∆ t=1 h 10 min
    3. A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as
    a function of time t by the equation x(t)=at²-bt³, a=1.5m/s² and b=0.05 m/s³.
    Calculate the average velocity of the car for the following time intervals:
    a) t=0 to t=2s
    b) t=0 to t=4s
    c) t=2 to t=4s

    total distance travelled


    v ave =
    time elapsed

    a.) x o=x ( 0 )=a t 2−bt 3=0 m; x f =x ( 2 )=¿

    (x ¿ ¿ f −x o )
    v ave = ¿
    2s

    (5.6 m−0 m)
    v ave =
    2s

    v ave =2.8 m/s

    b.) x o=x ( 0 )=a t 2−bt 3=0 m; x f =x ( 4 )=¿

    (x ¿ ¿ f −x o )
    v ave = ¿
    4s

    (20.8 m−0 m)
    v ave =
    4s

    v ave =5.2m/s
    c.) x o=x ( 2 )=¿

    x f =x ( 4 )=¿

    (x ¿ ¿ f −x o )
    v ave = ¿
    2s

    (20.8 m−5.6 m)
    v ave =
    2s

    v ave =7.6 m/s

    4. A car is stopped at a traffic light. It then travels along a straight road so that the distance from
    the light is given by x(t) = bt²-ct³, where b=2.4 m/s² and c = 0.12 m/s³.
    a) Calculate the average velocity of the car for the time interval t=0 to t=10s.
    b) Calculate the instantaneous velocity of the car at i) t=0; ii) t=5s; iii) t=10s
    c) How long after starting from rest is the car again at rest?

    total distance travelled


    a.) v ave =
    time elapsed

    x o=x ( 0 )=b t 2−c t 3=0 m; x f =x (10 )=¿

    (x ¿ ¿ f −x o )
    v ave = ¿
    10 s

    (120 m−0 m)
    v ave =
    10 s

    v ave =12m/s

    dx
    b.) v ( t )= =2bt−3 c t 2
    dt
    i) v ( 0 )=2 b ( 0 )−3 c ( 0 )=0 m/ s

    ii) v ( 5 ) =2¿

    ii) v ( 10 ) =2¿

    c.) x=b t 2−c t 3

    0=b t 2−c t 3

    0=t 2 (b−c t)

    t 2=0 ; b−ct=0

    b=ct

    b 2.4 m/s 2
    t= =
    c 0.12 m/s3

    t=20 s

    5. The human body can survive a negative acceleration trauma incident (sudden stop) if the
    magnitude of the acceleration is less than 250 m/s² (approximately 25g). If you are in an
    automobile accident with an initial speed of 105 km/h (65 mi/h) and are stopped by an airbag
    that inflates from the dashboard, over what distance must the airbag stop you for you to survive
    the crash?

    g=−250 m/ s2 ; v o =105 km/h ; v f =0

    v 2f =v 2o +2 gS

    v 2f −v 2o
    S=
    2g

    S=0−¿ ¿

    S=1.701m

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