Physics problems: kinematics

Motion with constant speed

Average speed

Instantaneous speed


Problem 1.

A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.?



Problem 3.

A car travels up a hill at a constant speed of 37 km/h and returns down the hill at a constant speed of 66 km/h. Calculate the average speed for the whole trip.



Problem 8.

We drive a distance of 1 km at 16 km/h. Then we drive an additional distance of 1 km at 32 km/h. What is our average speed?



Problem 15.

In reaching her destination, a backpacker walks with an average velocity of 1 m/s, due west. This average velocity results, because she hikes for 6 km with an average velocity of 3 m/s due west, turns around, and hikes with an average velocity of 0.3 m/s due east.

How far east did she walk (in kilometers)?



Problem 16.

It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to museum entrance. What is your displacement?



Problem 18.

An athlete swims the length of a 50.0-m pool in 20.0s and makes the return trip to the starting position in 22.0s. Determine her average velocities in

(a) the first half of the swim,

(b) the second half of the swim, and

(c) the round trip.







Problem 23.

A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?



Problem 24.

The slowest animal ever discovered is a crab found in the Red Sea that travels an average speed of 5.7 km/year. How long will it take this crab to travel 1 meter?



Problem 25.

A "moving sidewalk" in a busy airport terminal moves 1 m/s and is 200 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?



Problem 26.

Assume it takes 8 minutes to fill a 35.0 gal gasoline tank. (1 U.S. gal = 231 cubic inches)
(a) Calculate the rate at which the tank is filled in gallons per second.
(b) Calculate the rate at which the tank is filled in cubic meters per second.
(c) Determine the time interval, in hours, required to fill a volume at the same rate.



Problem 28.

A car travels east at 89 km/h for 1 h. It then travels 26° east of north at 141 km/h for 1 h.

(a) What is the average speed for the trip?

(b) What is the average velocity for the trip?



Problem 29.

(a) If a particle's position is given by   (where t is in seconds, and x is in meters), what is it's velocity at t=1s? 

(b) what is it's speed at t=1s? 

(c) Is there ever an instant when the velocity is 0?  If so, give the time.







Problem 35.

A rock is dropped from rest into a well.

(a) The sound of the splash is heard 4 s after the rock is released from rest.

How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s).

(b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?



Problem 37.

A displacement, s, of an object as a function of time, t, is given by

a) Find an expression for the acceleration of the object

b) Explain why this expression indicates that the acceleration is not constant



Problem 42.

A bicycle travels 3.2 km due east in 0.1 h, the 3.2 km at 15.0 degrees east of north in 0.21 h, and finally another 3.2km due east in 0.1 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?



Problem 49.

If it takes a player 3 seconds to run from the batter's box to the first base at an average speed of 6.5 m/s, what is the distance she covers in that time?



Problem 50.

A car goes down a certain road at an average speed of 40 km/h and returns along the same road at an average speed of 60 km/h.  Calculate the average speed for the round trip.



Problem 52.

(Inquiry into Physics-5th ed.,Ostdiek,Bord) A runner has an average speed of 4 m/s during a race. How far does the runner travel in 20 minutes?







Problem 56.

Does the odometer of a car measure a scalar or a vector quantity?



Problem 57.

The speed of light is about . Convert it into miles per hour (mph).



Problem 62.

A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 3.00 min. The tortoise wins by 10 cm.

(a) How long does the race take?

(b) What is the length of the race?



Problem 63.

Emily takes a trip, driving with a constant velocity of 90 km/h to the north except for a 30 min rest stop. If Emily's average velocity is 75 km/h to the north, how long does the trip take?



Problem 64.

To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event to qualify?



Problem 67.

(a) One liter ( ) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the (roughly circular) oil slick. Assume the oil molecules have a diameter of .

(b) Recalculate for the Exxon Valdez oil spill (March 1989), in which 11 million gallons (42 million L) of crude oil coated Prince William Sound in Alaska.







Problem 69.

An automobile traveling 90 km/h overtakes a 1.5-km-long train traveling in the same direction on a track parallel to the road. If the train's speed is 70 km/h,

(a) how long does it take the car to pass it, and

(b) how far will the car have traveled in the time?



Problem 80.

You travel on the highway at a rate of 60 mph for 1 hour and at 50 mph for 2 hours and 40 mph for 3 hours. What is the total distance you have traveled? What is your average speed during the trip?



Problem 86.

A body covers 1/4 journey with a speed of 40 km/h, 1/2 of it with 50 km/h and remaining with the speed of 60 km/h. Calculate average speed for entire journey.



Problem 96.

A particle  moves along the curve   with constant speed . Express its velocity as a function of (x,y).



Problem 115.

Two boys are racing for chocolates. The older one has a speed of 1 m/s and the younger one has a 0.5 m/s. The older one told the younger one to run first, which the younger one does. Ten seconds later the older one follows. How far would they be from the starting line for the older one to overtake the younger one?



Problem 120.

A car travels along a straight line. For the first half it travels 20 km/h and for second half it travels 50 km/h. What is the mean speed of that car?





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