Question 1

Which of the following best describes the difference between average velocity and instantaneous velocity?

Accepted Answer

Average velocity is the total displacement divided by total time, while instantaneous velocity is the velocity at a specific instant.

Question 2

A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1 (in $$meters, with $$t in $$seconds). What is the car's instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = 26 m/s$$

Question 3

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Question 4

A ball is thrown straight up with an initial velocity of $$v_0 = 20$ m/s. Neglecting air resistance, what is the maximum height reached by the ball? (Use g = 9.8$ m/s^2$)

Accepted Answer

$$h = 20.4 m$$

Question 5

Which of the following is a correct application of the particle model in physics?

Accepted Answer

Treating a car as a single point mass when analyzing its motion along a highway.

Question 6

A runner accelerates uniformly from rest to a speed of $$8 m/s in$$ $$4$$ seconds. What is the runner's acceleration?

Accepted Answer

$$a = 2 m/s$^2$$

Question 7

Which of the following best describes the area under a velocity vs. time graph?

Accepted Answer

It represents the object's displacement.

Question 8

A projectile is launched horizontally from a cliff with a speed of $$15 m/s. If $$the cliff is $$45 m $$high, how far from the base of the cliff does the projectile land? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$d = 30 m$$

Question 9

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 10

A cyclist travels 3 km east, then 4 km north. What is the magnitude of the cyclist's displacement?

Accepted Answer

$$5 km$$

Question 11

A car travels at $$30 m/s $$for $$10$$ seconds, then at $$10 m/s $$for $$20$$ seconds. What is the car's average speed over the entire trip?

Accepted Answer

$$16.7 m/s$$

Question 12

Which of the following is the correct way to add two vectors graphically?

Accepted Answer

Place the tail of the second vector at the head of the first vector.

Question 13

A ball rolls down a ramp with constant acceleration. If it starts from rest and travels $$5 m in$$ $$2 s$$, what is its acceleration?

Accepted Answer

$$a = 2.5 m/s$^2$$

Question 14

Which of the following is a correct statement about significant figures?

Accepted Answer

The number of significant figures in a measurement reflects the precision of the measurement.

Question 15

A boat moves north at $$5 m/s $$relative to the water. The river flows east at $$3 m/s. $$What is the boat's speed relative to the ground?

Accepted Answer

$$
$$ $$v = \sqrt{5^2$ + 3^2$} = 5.83 m/s$$

Physics with Calculus: Motion, Kinematics, and Vectors – Exam 1 Study Guide

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