Problem Set 2.6: | 1 | 3 | 5 | 7 | 9 | 13 | 15 | Go up
 - by Kelly Intile, 2003

1. What must be your average speed in order to travel 230 km in 3.25 hours? 

v_av  = Ds/Dt

distance = 230 km and time = 3.25 hours so average speed is 230/3.25, or 70.8 km/hr.
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3. If you are driving 110 km/hr along a straight road and you look to the side for 2.0 sec, how far do you travel during this period? 

v_av  = Ds/Dt

The only tricky part of this problem is to remember to keep your time units the same.  Divide your speed in km/hr by 3.6 and you get m/s.

110/3.6 =  30.555556 m/s

Now use 30.555556 as your velocity and 2.0 as your time and solve for displacement.  s = 61 m.
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5. You are driving home from school steadily at 65 mph for 130 miles.  It begins to rain and you slow to 55 mph.  You arrive home after driving 3 hours and 20 minutes.  (a) How far is your hometown from school?  (b) What was your average speed?

(a)  First, figure out how long it took to travel the first 130 miles.  v = s/t.  v = 65 and s = 130.  Solve for t and you get that the first 130 miles took 2 hours.  Since the whole trip took 3 hours and 20 minutes, you know that 1 hour and 20 minutes was spent driving in the rain at 55 mph.  Since you know time (1.3333 hrs) and speed (55 mph), you can figure out how much distance you covered in the second part of the trip.  v = s/t.  v = 55 and t = 1.3.  Solve for s and you find that you drove 73.333 miles in the rain.

You can add these distances together to find out how far you traveled altogether

73.333 + 130 = 203.333 miles = 203 miles

(b)  Average speed is total distance/total time.  You just figured out the total distance (203.333 miles) and the total time was given (3.3333 hours).  Divide these two.  Average speed = 60.999 mph = 61 mph.
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7. A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 minutes.  Calculate (a) the average speed and (b) the average velocity.

The important thing to notice here is that average speed means distance/time and average velocity means displacement/time.  

(a)  First we must figure out how much distance the jogger covered.  Eight times around .25 miles = 2 miles.  The book wants your answer in m/s so we must convert 2 miles to meters.  1 mile = 1.61 km, so 2 miles = 3.22 km.  3.22 km*1000 = 3220 m.

Now we need to know how much time it took.  We need to take the time they gave us (12.5 minutes) and convert it to seconds.            12.5 * 60 = 750 sec.

Now we can figure out speed.  distance/time = 3220 m / 750 sec = 4.29 m/s

(b)  Now we have to consider the displacement, not the distance.  Remember that displacement means how far (and in what direction) you are now from where you started.  If someone jogs eight complete laps, then they end up right where they first started.  Since displacement = 0, velocity = 0.
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9. Two locomotives approach each other on parallel tracks.  Each has a speed of 95 km/h with respect to the ground.  If they are initially 8.5 km apart, how long will it be before they reach each other? (See Fig. 2-28) 

<Fig 2-28>

Since their velocities are the same and they are headed directly towards each other, we can logically assume that they will meet at a point that is halfway between where they started.  This point is 8.5/2 = 4.25 km away from each train.  So all we really need to worry about is how long it takes one train to travel 4.25 km.

v_av  = Ds/Dt  v = 95 km/h and s = 4.25 km, so solve for time and you will get t = .044737 hrs.  .044737 * 60 = 2.7 min.
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13.  A sports car accelerates from rest to 95 km/h in 6.2 sec.  What is its average acceleration in m/s/s? 

a_av  = Dv/Dt

 First we need to change 95 km/hr to m/s.  95/3.6 = 26.3889 m/s

Dv means change in velocity.  If we started at 0 m/s and ended at 26.3889 m/s, then Dv = + 26.3889 m/s.  We know time is 6.2 seconds.  a = v/t.    26.3889 / 6.2 = 4.3 m/s/s.
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15.  A sprinter accelerates from rest to 10.0 m/s in 1.35 sec.  What is her acceleration (a) in m/s/s, and (b) in km/h/h? 

(a) Change in velocity is from 0 to 10, so it's 10.0 m/s.  Time is 1.35 sec.  a = v/t = 10/1.35 = 7.41 m/s/s

(b) Now we have to convert our velocity to km/h and our time to hours.

Multiply by 3.6 to go from m/s to km/h.  10.0*3.6 = 36 km/h

Divide seconds by 3600 to get hours.  1.35/3600 = .000375 hrs.

Now we can use the acceleration formula.  a = v/t.  v = 36 km/h and t = .000375 hr.  

36/.000375 = 96000 km/h/h = 9.60*10^4 km/h/h
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