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Motion in a straight line exercises · Physics Playground

ExercisesPhysics

Motion in a straight line

40 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Position & Velocity, Acceleration, Free Fall

Physics2.1 Relative Motion, Distance, and Displacement

ExampleCalculating Distance and DisplacementA cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement?With a figure

Physics2.2 Speed and Velocity

ExampleCalculating Average SpeedA marble rolls 5.2 m in 1.8 s. What was the marble's average speed?
ExampleCalculating Average VelocityA student has a displacement of 304 m north in 180 s. What was the student's average velocity?
ExampleSolving for Displacement when Average Velocity and Time are KnownLayla jogs with an average velocity of 2.4 m/s east. What is her displacement after 46 seconds?
ExampleSolving for Time when Displacement and Average Velocity are KnownPhillip walks along a straight path from his house to his school. How long will it take him to get to school if he walks 428 m west with an average velocity of 1.7 m/s west?

Physics2.3 Position vs. Time Graphs

ExampleUsing Position–Time Graph to Calculate Average Velocity: Jet CarFind the average velocity of the car whose position is graphed in Figure 1.13.
ExampleUsing Position–Time Graph to Calculate Average Velocity: Jet Car, Take TwoCalculate the instantaneous velocity of the jet car at a time of 25 s by finding the slope of the tangent line at point Q in Figure 2.13.

Physics2.4 Velocity vs. Time Graphs

ExampleUsing Velocity Graph to Calculate Some Stuff: Jet CarUse this figure to (a) find the displacement of the jet car over the time shown (b) calculate the rate of change (acceleration) of the velocity. (c) give the instantaneous velocity at 5 s, and (d) calculate the…
ExampleUsing Curvy Velocity Graph to Calculate Some Stuff: Jet Car, Take TwoUse Figure 2.19 to (a) find the approximate displacement of the jet car over the time shown, (b) calculate the instantaneous acceleration at t = 30 s, (c) find the instantaneous velocity at 30 s, and (d) calculate…

Physics3.1 Acceleration

ExampleAn Accelerating Subway TrainA subway train accelerates from rest to 30.0 km/h in 20.0 s. What is the average acceleration during that time interval?
ExampleAn Accelerating Subway TrainNow, suppose that at the end of its trip, the train slows to a stop in 8.00 s from a speed of 30.0 km/h. What is its average acceleration during this time?

Physics3.2 Representing Acceleration with Equations and Graphs

ExampleAcceleration of a DragsterThe time it takes for a dragster to cross the finish line is unknown. The dragster accelerates from rest at 26 m/s2 for a quarter mile (0.250 mi). What is the final velocity of the dragster?
ExampleFalling Objects (part 1)A person standing on the edge of a high cliff throws a rock straight up with an initial velocity v0 of 13 m/s. (a) Calculate the position and velocity of the rock at 1.00, 2.00, and 3.00 seconds after it is thrown.…
ExampleFalling Objects (part 2)(b) Make graphs of position versus time, velocity versus time, and acceleration versus time. Use increments of 0.5 s in your graphs.

College Physics2.1 Displacement

Quick checkA cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement?

College Physics2.2 Vectors, Scalars, and Coordinate Systems

Quick checkA person’s speed can stay the same as he or she rounds a corner and changes direction. Given this information, is speed a scalar or a vector quantity? Explain.

College Physics2.3 Time, Velocity, and Speed

Quick checkA commuter train travels from Baltimore to Washington, DC, and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. What is (a) the average velocity of the train, and (b)…

College Physics2.4 Acceleration

Example 2.1Calculating Acceleration: A Racehorse Leaves the GateA racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration? Figure 2.15 (credit: Jon Sullivan, PD Photo.org)With a figure
Example 2.2Calculating Displacement: A Subway TrainWhat are the magnitude and sign of displacements for the motions of the subway train shown in parts (a) and (b) of Figure 2.18?
Example 2.3Comparing Distance Traveled with Displacement: A Subway TrainWhat are the distances traveled for the motions shown in parts (a) and (b) of the subway train in Figure 2.18?
Example 2.4Calculating Acceleration: A Subway Train Speeding UpSuppose the train in Figure 2.18(a) accelerates from rest to 30.0 km/h in the first 20.0 s of its motion. What is its average acceleration during that time interval?
Example 2.5Calculate Acceleration: A Subway Train Slowing DownNow suppose that at the end of its trip, the train in Figure 2.18(a) slows to a stop from a speed of 30.0 km/h in 8.00 s. What is its average acceleration while stopping?
Example 2.6Calculating Average Velocity: The Subway TrainWhat is the average velocity of the train in part b of Example 2.2, and shown again below, if it takes 5.00 min to make its trip? Figure 2.22With a figure
Example 2.7Calculating Deceleration: The Subway TrainFinally, suppose the train in Figure 2.22 slows to a stop from a velocity of 20.0 km/h in 10.0 s. What is its average acceleration?
Quick checkAn airplane lands on a runway traveling east. Describe its acceleration.

College Physics2.5 Motion Equations for Constant Acceleration in One Dimension

Example 2.8Calculating Displacement: How Far does the Jogger Run?A jogger runs down a straight stretch of road with an average velocity of 4.00 m/s for 2.00 min. What is his final position, taking his initial position to be zero?
Example 2.9Calculating Final Velocity: An Airplane Slowing Down after LandingAn airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s^2 for 40.0 s. What is its final velocity?
Example 2.10Calculating Displacement of an Accelerating Object: DragstersDragsters can achieve average accelerations of 26.0 m/s^2. Suppose such a dragster accelerates from rest at this rate for 5.56 s. How far does it travel in this time? Figure 2.31 U.S. Army Top Fuel pilot Tony “The…With a figure
Example 2.11Calculating Final Velocity: DragstersCalculate the final velocity of the dragster in Example 2.10 without using information about time.
Example 2.12Calculating Displacement: How Far Does a Car Go When Coming to a Halt?On dry concrete, a car can decelerate at a rate of 7.00 m/s^2, whereas on wet concrete it can decelerate at only 5.00 m/s^2. Find the distances necessary to stop a car moving at 30.0 m/s (about 110 km/h) (a) on dry…
Example 2.13Calculating Time: A Car Merges into TrafficSuppose a car merges into freeway traffic on a 200-m-long ramp. If its initial velocity is 10.0 m/s and it accelerates at 2.00 m/s^2, how long does it take to travel the 200 m up the ramp? (Such information might be…
Quick checkA rocket accelerates at a rate of 20 m/s^2 during launch. How long does it take the rocket to reach a velocity of 400 m/s?

College Physics2.7 Falling Objects

Example 2.14Calculating Position and Velocity of a Falling Object: A Rock Thrown UpwardA person standing on the edge of a high cliff throws a rock straight up with an initial velocity of 13.0 m/s. The rock misses the edge of the cliff as it falls back to earth. Calculate the position and velocity of…
Example 2.15Calculating Velocity of a Falling Object: A Rock Thrown DownWhat happens if the person on the cliff throws the rock straight down, instead of straight up? To explore this question, calculate the velocity of the rock when it is 5.10 m below the starting point, and has been…
Example 2.16Find g from Data on a Falling ObjectThe acceleration due to gravity on Earth differs slightly from place to place, depending on topography (e.g., whether you are on a hill or in a valley) and subsurface geology (whether there is dense rock like iron…With a figure
Quick checkA chunk of ice breaks off a glacier and falls 30.0 meters before it hits the water. Assuming it falls freely (there is no air resistance), how long does it take to hit the water?

College Physics2.8 Graphical Analysis of One-Dimensional Motion

Example 2.17Determining Average Velocity from a Graph of Position versus Time: Jet CarFind the average velocity of the car whose position is graphed in Figure 2.47.
Example 2.18Determining Instantaneous Velocity from the Slope at a Point: Jet CarCalculate the velocity of the jet car at a time of 25 s by finding the slope of the x vs. t graph in the graph below. Figure 2.50 The slope of an x vs. t graph is velocity. This is shown at two points. Instantaneous…With a figure
Example 2.19Calculating Acceleration from a Graph of Velocity versus TimeCalculate the acceleration of the jet car at a time of 25 s by finding the slope of the v vs. t graph in Figure 2.51(a).
Quick checkA graph of velocity vs. time of a ship coming into a harbor is shown below. (a) Describe the motion of the ship based on the graph. (b)What would a graph of the ship’s acceleration look like? Figure 2.52With a figure