Acceleration Problems

 

1.     A skier accelerates at 1.20 m/s2 down an icy slope, starting from rest. How far does she get in 5.0 s?

                                                                                                                                                          15 m

2.     What is the acceleration of an object that accelerates steadily from rest, traveling 10 m in 10 s?

                                                                                                                                                   0.20 m/s2

3.     A car enters a tunnel at 24 m/s and accelerates steadily at 2.0 m/s2. At what velocity does it leave the tunnel, 8.0 s later?

                                                                                                                                                       40 m/s

4.     How long does it take an airplane, accelerating from rest at 5.0 m/s2, to travel 360 m?

                                                                                                                                                           12 s

5.     The driver of a truck moving at 18 m/s throws on its brakes and stops it in 4.0 s. What is the acceleration of the truck?

                                                                                                                                                   -4.5 m/s2

6.     A motorcycle stuntman accelerates from rest to a maximum velocity of 35.2 m/s at the top of the take-off ramp, then swoops up and over 20 cars. Calculate how long it takes him to accelerate, at an acceleration of 8.8 m/s2.

                                                                                                                                                          4.0 s

7.     Here is the velocity-time graph of a trip on a bicycle.

How fast is the bicycle moving at each of the following time?

a) 4 s   4 m/s   b) 6 s  6 m/s   c) 10 s  3.4 m/s           d) 12 s  2 m/s

What is the acceleration of the bicycle at each of these times?

a) 2 s   0 m/s2  b) 5 s   1.0 m/s2           c) 7 s   -0.67 m/s2        d) 14 s  0.75 m/s2

 

8.     If an electron inside a TV tube accelerates from rest to 1/10c (where c is the speed of light), in a space of 5.0 cm, what is its acceleration? c = 3.00 x 108 m/s therefore 1/10c is 3.00 x 107 m/s ;                                                                                                                   a = 9.0 x 1015  m/s2

 

9.     Two runners accelerate uniformly from rest at 1.40 m/s2 for 8.00 s.

a)     What is their final velocity? 11.2 m/s

b)    What is their average velocity? 5.6 m/s

c)     How far do they run? 44.8 m

 

10.  A car accelerates from rest at 6.00 m/s2. How far does it get between 10.0 s and 15.0 s?

                  At 10 s d = 300 m, at 15 s d = 675 m, therefore d between 10 and 15 seconds is 375 m

11.  A skier accelerates steadily down a hill from 3.50 m/s to 11.40 m/s in 4.20 s. a = 1.88 m/s2

a)     What is the average velocity for the trip? 7.45 m/s

b)    What is the displacement? 31.3 m

 

12.  Jack and Jill ran down the hill. Both started from rest and accelerated steadily. Jack accelerated at 0.25 m/s2 and Jill at 0.30 m/s2. After running for 20.0 s, Jill fell down.

a)     How far did Jill get before she fell? 60 m

b)    How far had Jack traveled when Jill fell? 50 m

c)     How fast was Jack running when Jill fell? 5 m/s

d)    How long was it after Jill fell that Jack ran into her and broke his crown (to the nearest second)?    1.9 s longer

 

13.  The graph shows the motion of a small bird flying down a long, straight, narrow cage.

a)     What is the birdŐs acceleration for the first 10 s of the trip? Nearly a straight line, so 0.5 m/s2

b)    At what time is the birdŐs acceleration at its maximum? Find steepest part of graph, at about 20-23 s

c)     What is this maximum acceleration? About 1.3 m/s2

d)    At what time(s) is the birdŐs acceleration zero? At the top of the curve, so about 29 s

e)     At what time(s) is the birdŐs velocity zero? At time zero.

 

14.  Spiderman is crawling up a building at the rate of 0.50 m/s. Seeing Spiderwoman 56 m ahead of him; he accelerates at the rate of 2.3 m/s2.

a)     How fast will he be moving when he reaches Spiderwoman? 16.1 m/s

b)    How much time will it take to reach Spiderwoman? 6.8 s

c)     When he reaches Spiderwoman, Spiderman discovers she is a Black Widow and, as you know, Black Widows eat their mates! He is 200.0 m from the road below. How long will it take to fall to the safety of the road, if he drops with an acceleration of g = 9.80 m/s2? 6.4 s

d)    Why will Spiderman not be killed by the fall? He has spider-like senses and can whip out that web from his wrist to slow himself down