⚙️ Unit 1: Kinematics — Practice Quiz

Assessment AS Learning — Self-Check (SPH3U)
🔄 Not Graded — Unlimited Retakes
Purpose: Test your understanding of 1-D and 2-D motion, vectors, free fall, projectile motion, and relative velocity. Instant feedback with worked solutions on every question.

📋 Formula Reference

\( v = v_0 + at \)  |  \( d = v_0 t + \tfrac{1}{2}at^2 \)  |  \( v^2 = v_0^2 + 2ad \)  |  \( d = \tfrac{1}{2}(v_0+v)t \)
\( g = 9.8 \text{ m/s}^2 \)  |  Range \( R = v_0^2\sin(2\theta)/g \)  |  \( c^2 = a^2+b^2 \)
Score: 0 / 10
Question 1 — Average velocity
A jogger runs 800 m east in 4.0 min, then 400 m west in 2.0 min. What is the average velocity for the whole trip?
Answer: m/s [E]
Solution:
Net displacement: \( 800 - 400 = 400 \text{ m east} \)
Total time: \( 4.0 + 2.0 = 6.0 \text{ min} = 360 \text{ s} \)
\( v_\text{avg} = 400/360 = 1.11 \text{ m/s [E]} \)
Question 2 — Uniform acceleration
A car accelerates uniformly from \(8.0\) m/s to \(28\) m/s over a distance of \(120\) m. What is the acceleration?
Answer: m/s²
Solution:
Use \( v^2 = v_0^2 + 2ad \):
\( 28^2 = 8^2 + 2a(120) \)
\( 784 = 64 + 240a \)
\( a = 720/240 = 3.0 \text{ m/s}^2 \)
Question 3 — Free fall
A stone is dropped from a cliff and hits the water \(2.5\) s later. How tall is the cliff (assume air resistance negligible)?
Answer: m
Solution:
\( d = \tfrac{1}{2}gt^2 = \tfrac{1}{2}(9.8)(2.5)^2 = 30.6 \text{ m} \)
Question 4 — Vector addition
A hiker walks \(6.0\) km east then \(8.0\) km north. What is the magnitude of the displacement?
Answer: km
Solution:
\( |\vec d| = \sqrt{6^2 + 8^2} = \sqrt{36+64} = \sqrt{100} = 10.0 \text{ km} \)
Question 5 — Horizontal projectile
A ball is thrown horizontally at \(15\) m/s from a cliff \(45\) m high. How long does it take to hit the ground?
Answer: s
Solution:
Vertical motion: \( 45 = \tfrac{1}{2}(9.8)t^2 \) so \( t^2 = 9.18 \), \( t = 3.03 \text{ s} \)
Question 6 — Projectile range (angle launch)
A football is kicked at \(20\) m/s at \(30°\) above the horizontal. What is its range on level ground?
Answer: m
Solution:
\( R = v_0^2 \sin(2\theta)/g = 20^2 \sin(60°)/9.8 = 400(0.866)/9.8 = 35.3 \text{ m} \)
Question 7 — Maximum height
For the kick in Q6, what maximum height does the ball reach?
Answer: m
Solution:
\( v_{0y} = 20\sin(30°) = 10 \text{ m/s} \)
At apex \( v_y=0 \): \( 0 = 10^2 - 2(9.8)H \), so \( H = 100/19.6 = 5.10 \text{ m} \)
Question 8 — Relative velocity (river crossing)
A boat heads directly across a river at \(4.0\) m/s relative to the water. The current flows downstream at \(3.0\) m/s. What is the boat's resultant speed relative to the shore?
Answer: m/s
Solution:
Velocities are perpendicular: \( v = \sqrt{4^2+3^2} = \sqrt{25} = 5.0 \text{ m/s} \)
Question 9 — Concept (multiple choice)
A ball thrown straight up returns to the thrower's hand. At the highest point of its motion, which statement is correct?
Solution:
At the apex the ball is momentarily at rest (\( v=0 \)) but gravity continues to accelerate it downward at \( g = 9.8 \) m/s², which is what brings it back down.
Question 10 — Stopping distance
A car travelling at \(25\) m/s applies the brakes and decelerates uniformly at \(5.0\) m/s². How far does the car travel before stopping?
Answer: m
Solution:
\( v^2 = v_0^2 + 2ad \): \( 0 = 25^2 + 2(-5)d \), so \( d = 625/10 = 62.5 \text{ m} \)