⚙️ Unit 1: Dynamics — Practice Quiz

Assessment AS Learning — Self-Check
🔄 Not Graded — Unlimited Retakes
Purpose: Test your understanding of kinematics, forces, friction, and circular motion. Instant feedback on every question.

📋 Formula Reference

\( v = v_0 + at \)  |  \( d = v_0 t + \tfrac{1}{2}at^2 \)  |  \( v^2 = v_0^2 + 2ad \)  |  \( \Sigma F = ma \)
\( f = \mu N \)  |  \( F_c = \frac{mv^2}{r} \)  |  \( g = 9.8 \text{ m/s}^2 \)
Score: 0 / 10
Question 1
A car accelerates uniformly from rest to \( 25 \text{ m/s} \) in \( 5.0 \text{ s} \). What is its acceleration?
Answer: m/s²
Solution:
\( a = \frac{\Delta v}{\Delta t} = \frac{25 - 0}{5.0} = 5.0 \text{ m/s}^2 \)
Question 2
A ball is thrown horizontally at \( 15 \text{ m/s} \) from a cliff \( 45 \text{ m} \) high. How long does it take to hit the ground?
Answer: s
Solution:
Vertical: \( d = \frac{1}{2}gt^2 \)
\( 45 = \frac{1}{2}(9.8)t^2 \)
\( t^2 = \frac{45}{4.9} = 9.18 \)
\( t = 3.03 \text{ s} \)
Question 3
A \( 10 \text{ kg} \) box is pushed with \( 50 \text{ N} \) across a floor. The coefficient of kinetic friction is \( \mu_k = 0.30 \). What is the acceleration?
Answer: m/s²
Solution:
\( N = mg = 10 \times 9.8 = 98 \text{ N} \)
\( f = \mu_k N = 0.30 \times 98 = 29.4 \text{ N} \)
\( F_{net} = 50 - 29.4 = 20.6 \text{ N} \)
\( a = \frac{F_{net}}{m} = \frac{20.6}{10} = 2.06 \text{ m/s}^2 \)
Question 4
Which of Newton's laws explains why you feel pushed back into your seat when a car accelerates?
Solution:
Newton's 1st Law (inertia): Your body tends to remain at rest while the car accelerates forward. You feel "pushed back" because the seat pushes you forward but your body resists the change in motion.
Question 5
An object on a frictionless inclined plane (angle \( 30° \)) has mass \( 5.0 \text{ kg} \). What is the acceleration down the incline?
Answer: m/s²
Solution:
\( a = g \sin\theta = 9.8 \times \sin(30°) = 9.8 \times 0.5 = 4.9 \text{ m/s}^2 \)
Note: mass cancels out — acceleration on a frictionless incline depends only on the angle.
Question 6
A \( 0.50 \text{ kg} \) ball on a string moves in a horizontal circle of radius \( 1.2 \text{ m} \) at \( 4.0 \text{ m/s} \). What is the centripetal force?
Answer: N
Solution:
\( F_c = \frac{mv^2}{r} = \frac{0.50 \times 4.0^2}{1.2} = \frac{8.0}{1.2} = 6.67 \text{ N} \)
Question 7
Two blocks (\( 3 \text{ kg} \) and \( 5 \text{ kg} \)) are in contact on a frictionless surface. A force of \( 24 \text{ N} \) pushes on the \( 3 \text{ kg} \) block. What is the force between the blocks?
Answer: N
Solution:
System: \( a = \frac{F}{m_1 + m_2} = \frac{24}{3+5} = 3.0 \text{ m/s}^2 \)
Force on 5 kg block: \( F_{contact} = m_2 \times a = 5 \times 3.0 = 15.0 \text{ N} \)
Question 8
A car goes over a hill (radius of curvature \( 50 \text{ m} \)) at \( 20 \text{ m/s} \). The driver's mass is \( 70 \text{ kg} \). What normal force does the seat exert on the driver at the top?
Answer: N
Solution:
At the top of the hill: \( mg - N = \frac{mv^2}{r} \)
\( N = mg - \frac{mv^2}{r} = 70(9.8) - \frac{70(20)^2}{50} = 686 - 560 = 126 \text{ N} \)
The normal force is reduced — this is why you feel lighter going over a hill.
Question 9
Which of the following is NOT a real force?
Solution:
Centrifugal force is a fictitious (pseudo) force that only appears in rotating (non-inertial) reference frames. In an inertial frame, objects moving in a circle need a real centripetal force directed inward — there is no outward force.
Question 10
A projectile is launched at \( 30° \) above the horizontal with initial speed \( 40 \text{ m/s} \). What is the maximum height reached?
Answer: m
Solution:
\( v_{0y} = 40 \sin(30°) = 20 \text{ m/s} \)
At max height, \( v_y = 0 \):
\( v_y^2 = v_{0y}^2 - 2gH \)
\( 0 = 20^2 - 2(9.8)H \)
\( H = \frac{400}{19.6} = 20.4 \text{ m} \)