Velocity and M/s

1. A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at an average speed of 40 km/h. The average speed of the car for this 80 km trip is:
A) 40 km/h
B) 45 km/h
C) 48 km/h
D) 53 km/h
E) 80 km/h

30’+60’ = 90’=5400s=1.5h
40km+40km=80km
vavg= 80000m/5400s=13.168724279835390946502057613169 m/s = 48 km/h

2. The coordinate of an object is given as a function of time by x = 7t – 3t2, where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:
A) 5 m/s
B) –5 m/s
C) 11 m/s
D) –11 m/s
E) –14.5 m/s

vt= 7-6t = 7-12=-5 m/s

3. The coordinate of a particle in meters is given by x(t) = 16t – 3.0t3, where the time t is in seconds. The particle is momentarily at rest at t =
A) 0.75 s
B) 1.3 s
C) 5.3 s
D) 7.3 s
E) 9.3 s

0=16-9t2 t2=16/9 t=1.33 s

4. Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t – 4.0t3, where t is in seconds. At the end of 1.0 s the acceleration of the auto is:
A) 27 m/s2
B) 4.0 m/s2
C) –4.0 m/s2
D) –12 m/s2
E) –24 m/s2

at= -24t

5. Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by | particle 1: x(t) = 3.5 – 2.7t3 | | particle 2: x(t) = 3.5 + 2.7t3 | | particle 3: x(t) = 3.5 + 2.7t2 | | particle 4: x(t) = 3.5 – 3.4t – 2.7t2 |
Which of these particles is speeding up for t> 0?
A) All four
B) Only 1
C) Only 2 and 3
D) Only 2, 3, and 4
E) None of them

6. A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s2 south. After 6 seconds its velocity will be:
A) 7 m/s north
B) 7 m/s south
C) 43 m/s north
D) 20 m/s north
E) 20 m/s south

v = v0 + at = 25+3x6= 43m/s

7. A particle goes from x = –2 m, y = 3 m, z = 1 m to x = 3 m, y = –1 m, z = 4 m. Its displacement is:
A)
B)
C)
D)
E)