2.2.2 Solving Problems Involving Motion Under Constant Acceleration

Question 1

note

Answer 1

• A race car is driven 25 m in 5 s. What is its velocity as it crosses the finish line? \
• You need to use the master equations of kinematics. The first two equations allow you to solve for vf, the final velocity.However, both of these equations require that you know the car’s acceleration (a), and the value of a is not given in the problem.
• Look at the third equation. You know the value of all the terms except for acceleration. If you let xi= 0 m, then xf= 25m. The car started at rest so . The time required for the trip, Dt, was 5 s. You can solve the third equation of kinematics for the car’s acceleration: .
• Substitute the value of the car’s acceleration into the first equation of kinematics and solve for the velocity of the car as it crosses the finish line: .
• You can check your answer using the second equation of kinematics. Notice that while the instantaneous velocity of the car as it crosses the finish line is , the car’s average velocity for the entire race is

Question 2

Which of the following is not one of the equations of kinematics with constant acceleration?

Answer 2

vf^2 = vi^2 + 2a delta t

Question 3

Suppose an object in motion is observed for a 10-second interval. During this time the object’s velocity increases from an initial velocity of 18 m/s and the object travels 317m. Given this information, what are the values for vf, a, and the average velocity, v?

Answer 3

vf = 45.4 m/s
a = 2.74 m^2/s
v = 31.7 m/s

Question 4

A moving object starts at a velocity of 4.0 m / s and and travels 35 m in a straight line with a constant acceleration of 8.0 m / s^2. How long did it take the object to complete this movement?

Answer 4

2.5 s

Question 5

Suppose a sprinter runs a 50 m race with a constant acceleration. The sprinter starts from rest and runs the race in 5 seconds. Which of the following is the sprinter’s final velocity?

Answer 5

20 m / s

Question 6

A squirrel sitting on a tree branch 17 m off the ground drops its acorn. Assume that the acorn has a constant acceleration of approximately 10 m / s2. How long will it take the acorn to hit the ground?

Answer 6

1.8 s

Question 7

Suppose an object initially at rest travels 32 cm in 4 seconds. The object’s acceleration is constant. What is the object’s average velocity during these 4 seconds?

Answer 7

8 cm / s

Question 8

Suppose you are in a car that starts at rest and goes 125 meters in 10 seconds with constant acceleration. What is your acceleration and instantaneous velocity at 10 seconds?

Answer 8

a = 2.5 m / s2
v = 25 m / s

Question 9

An object is observed for a 5 second interval. During this time, the object’s velocity increases from 2 m / s to a final velocity and the object travels 75 m. The acceleration of the object is constant. Given this information, which of the following statements is not correct?

Answer 9

The final velocity of the object is 26 m / s.

Question 10

What is the final velocity and the acceleration of a moving object that starts at a velocity of 115 m / s and travels 800 meters in 4 seconds? (Assume its acceleration is constant.)

Answer 10

a = 42.5 m / s2
v = 285 m / s