HW#1 (Basic Motion) Answers
1. What must be your car’s average speed in order to travel 235 km in 3.25 hours?
Avg. Speed = distance traveled/time
= 235 km/3.25 hr = 72.3 km/hr
2. A rolling ball moves from x1=3.4 cm to x2 = -4.2cm during the time from t1=3.0 s
to t2=6.1 s. What is its average velocity?
Avg. Velocity = displacement/time or (x2-x1) / (t2-t1)
= (-4.2 cm – 3.4 cm) / (6.1s – 3.0 s)
= -7.6 cm/3.1s
= -2.45 cm/s
3. You are driving home from school steadily at 95 km/h for 130 km. It then begins
to rain and you slow to 65 km/h. 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.
Time driving 95km/h can be found with (time = distance/speed)
Time = 130 km/95km/hr = 1.37 hours or 1 hour 22 min.
Total time of trip is 3 hr. 20 min. So, time driving 65 km/hr = 1 hour 58 min.
Distance traveled while driving 65km/hr can be found with (d = speed x time)
Distance = 65 km/hr x 1.97 hours = 128 km
Total distance traveled= 130 km + 128 km = 258 km
b. Avg. speed = distance/time = 258 km/ 3.33 hours = 77.5 km/hr
4. A horse canters away from its trainer in a straight line, moving 116 m away in
14.0s. It then turns abruptly and gallops halfway back in 4.8 s. Calculate (a) its
average speed and (b) its average velocity for the entire trip, using “away from the
trainer” as the positive direction.
a. Avg. speed = d/t so, (116m + 58m) / 14.0s + 4.8s = 9.26 m/s
b. Avg. velocity = displ./t so, (58m) / 18.8s = 3.09 m/s
5. A bowling ball traveling with constant speed hits the pins at the end of the
bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins
2.5 s after the ball is released from his hands. What is the speed of the ball? (The
speed of sound is 340 m/s)
Time for sound to travel 16.5 meters can be found with (t = d/v = 16.5m/340m/s)
= .049s
Time for ball to travel 16.5 meters = 2.5s - .049s = 2.451s
Speed of ball = 16.5m/2.451s = 6.73m/s
6. A sports car moving at constant speed travels 110 m in 5.0 s. If it then brakes and
comes to a stop in 4.0 s, what is its acceleration in m/s2?
Speed of car after 5.0 seconds = 110m/5.0s = 22m/s
Acceleration = change in velocity / change in time
= vf-vi/t
= (0m/s – 22m/s)/4.0s = -5.5m/s/s