Please help me doing my homework ... 1. Chapter 3, Problem 3 A driver in a hurry

Question

Please help me doing my homework ... 1. Chapter 3, Problem 3 A driver in a hurry decides to take a freeway that cuts straight across town. The freeways entrance and exit are 4.00mi apart. By weaving dangerously in and out of traffic, the driver manages to average 75mi/h from entrance to exit. How much time did the driver save by averaging 75 mi/h instead of 65 mi/h? Express your answer in the appropriate unit. 2. Chapter 3. Problem 4 A family drives 60.0mi/h for 3.00h. They then stop at a rest stop for 15.0min. Finally they drive the last 150mi in 3.50h. That is the magnitude of their average velocity for the trip? 3. Chapter 3, Problem 8 A driver brakes a minivan from 30.0mi/h to 20.0mi/h in 1.50s. What is the cars average acceleration? Express your answer in miles per hour per second and meters per second per second. 4. Chapter 3, Problem 22. An instant is one single point in time. An interval is an extended period of time. Consider the motion of an object represented by the position versus time graph in Figure 3.P7 (turn this sheet over or see page 71) a. List all instants when the object was stopped only for an instant b. List all intervals when the object was at rest. 5. Chapter 3, Problem 25 Consider the motion of an object represented by the velocity versus-time graph in Figure 3.P10. a. List al instants when the object was stopped only for an instant. b. List all intervals when the object was at rest. 6. Chapter 3, Problem 38 An arrow has a velocity of 45.0m/s when it reaches a straw target. a. It its tip comes to rest at a depth of 20.0cm, calculate its (assumed constant) average acceleration. b. How long after first touching the straw does it take the amow to come to rest? 7. Chapter 3, Problem 43 A laser scans a line of information initially at a rate of 25 m/s. The scan rate decreases uniformly to 1.05 m/s in 1.5h. What is the total length of the line of information scanned by the laser? 8. Chapter 3, Problem 67 A dragster completes the quarter mile in exactly 12.0s a. Calculate the dragster's acceleration. Express your answer in mph s and gs. b. How fast is the dragster going when it reaches the quarter-mile mark? c. If the dragster then brakes at 1.2g, how far goes it go before stopping? 9. Chapter 3, Problem 72 (sort of) A pitching machine can throw a baseball straight up at 80 mph from an initial height of l meter. a. high the baseball b. How much time elapses before the ball hits the ground? c, How fast is it moving when it hits the ground?

Explanation / Answer

1)
   distance between free way entrance and exit is 4 miles

   moving with 75 mph, 65 mph time save to move from entrance to exit is

   delta T = 4(1/65 -1/75)= 0.00820 h = 0.49 min = 29.538 s

time saving is 29.53 s

2) Average velocity per sec is delta V = total distance traveled / total time duration

       first 3 hours , distance covered is 3*60 = 180 miles,

       took rest about 15 min,

       last 3.5 hours traveled 150 miles
                    

   delta V = (180+150)/(3+0.25+3.5)= 48.89 miles ph = 78.224 kmph=21.72 m/s

3) when driver applies brakes

   car starts to decelerate here

   ma = m (v2-v1/t2-t2)
         a = (20 - 30)/1.5 = 6.66 miles /h s = 2.96 m/s2

4)    the object will be stopped only for an instant are at time 3s,7s,17s
   object will be stopped between the interval t= 10 to 15 s

  

6) using equations of motion

   v^2 - U^2 = 2*a*s ==> a = - u^2/2*s = 45^2/2*0.2= 2531.25 m/s2
         time t = 0.018s

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