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QUESTION: A bus is moving with a speed of 10 m/s on a straight road . A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should scooterist chase the bus?

ANSWER: Make the final positions of both the bus and the scooter the same.

For the bus the position is Dbus=10m/s*100s

For the scooter the position is Dscooter=V*100s-1000 (Since the scooter starts 1000m behind the bus.)

Make these equal:

10*100=V*100-1000

solving for the velocity:

V=20m/s

---------- FOLLOW-UP ----------

QUESTION: an object thrown vertically up from the ground passes the height 5 m twice in an interval of 10 s. what is its time of flight?[option:1)root 28 s 2)root 86 s 3)root 104 s 4)root 72 s ]

First calculate the velocity of the object as it passes the 5m mark:

do=5m, df=5m, vo=?, vf=?, a=-9.8m/s^2, t=10s

df=1/2*a*t^2+vo*t+do

5=-4.9*10^2+vo*10+5

Solving for the velocity as the object passes the 5m mark:

vo=49m/s

Now that we know the velocity as the object passes the 5m mark we can now solve for velocity with which the object leaves the ground using:

Vf^2=vo^2+2*a*dD

49^=vo^2-2*9.8*5

Solving for Vo:

Vo=sqrt(49^2+2*9.8*5)=50m/s

So the total flight time will be:

Do=0m, Df=0m, Vo=50m/s, Vf=-50m/s, a=-9.8m/s^2, t=?

df=1/2*a*t^2+vo*t+do

0=-4.9*t^2+50*t+0

t=10.2s

Which is the square root of 104, so c) is the correct answer.

Physics

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.