Exam 2: One-Dimensional Motion

In 2.0 s, a particle moving with constant acceleration along the x axis goes from x = 10 m to x = 50 m. The velocity at the end of this time interval is 10 m/s. What is the acceleration of the particle?

The speed of an object is given by v = 5.00t2 +4, where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s?

At t = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction. The acceleration of the particle varies with time as shown in the diagram. What is the velocity of the particle at t = 5.0 s? ​ ​

A particle is moving with a constant acceleration of 4.0 m/s². Its speed at t = 1.0 s is 4.0 m/s and at t = 3.0 s it is 12.0 m/s. What is the area under the position-time graph for the interval from t = 1.0 s to t = 3.0 s?

The position of a particle as it moves along the x axis is given for t > 0 by x = (t3 − 3t2 + 6t) m, where t is in s. Where is the particle when it achieves its minimum speed (after t = 0)?

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?

A ball thrown vertically from ground level is caught 3.0 s later when it is at its highest point by a person on a balcony which is 14 m above the ground. Determine the initial speed of the ball.

When starting from rest at the bottom of a straight road with constant upward slope, Joan bicycles to the top 50.0 s ahead of Sally, whose travel time is 5.00 minutes. What is the ratio of Joan's acceleration to Sally's acceleration?

A particle is moving at constant velocity. Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m. What is the slope of the position-time graph for this particle?

The area under a graph of vx vs. t from t = ti to t = tf represents

A bicyclist starts down a hill with an initial speed of 2.0 m/s. She moves down the hill with a constant acceleration, arriving at the bottom of the hill with a speed of 8.0 m/s. If the hill is 12 m long, how long did it take the bicyclist to travel down the hill?

A boy on a skate board skates off a horizontal bench at a velocity of 10 m/s. One tenth of a second after he leaves the bench, to two significant figures, the magnitudes of his velocity and acceleration are:

In 20 minutes, Kara ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval?

Two identical balls are at rest side by side at the bottom of a hill. Some time after ball A is kicked up the hill, ball B is given a kick up the hill. Ball A is headed downhill when it passes ball B headed up the hill. At the instant when ball A passes ball B,

A particle moving along the x axis has a position given by x = 54t − 2.0t3 m. At the time t = 3.0 s, the speed of the particle is zero. Which statement is correct?

A stone is thrown from the top of a building with an initial velocity of 20 m/s downward. The top of the building is 60 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground?

A peregrine falcon dives at a pigeon. The falcon starts with zero downward velocity and falls with the acceleration of gravity. If the pigeon is 76.0 m below the initial height of the falcon, how long does it take the falcon to intercept the pigeon?

The position of a particle as it moves along the x axis is given by x = 15e−2t m, where t is in s. What is the acceleration of the particle at t = 1.0 s?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct? ​

At t = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction. The acceleration of the particle varies with time as shown in the diagram. What is the position of the particle at t = 5.0 s?