PHYS 1112 Tutorial 1
Vector algebra review
The figure below shows a set of three vectors. The 𝑥- and 𝑦-axes are defined in the conventional way, as
are the Cartesian unit vectors 𝑖̂ and 𝑗̂. In addition, the grid lines are all spaced by unit length.
⃗ = 𝑎 − 𝑐. Draw 𝑃⃗ and 𝑄
⃗ in the grid below. Also express them in terms of
Define 𝑃⃗ = 2𝑎 + 𝑏⃗ and 𝑄
𝑖̂ and 𝑗̂.
Your answer:
𝑃⃗ = _________________________
⃗ = _________________________
𝑄
PHYS 1112 Tutorial 1
Calculus review
Note: Assume all quantities are in appropriate SI units unless otherwise stated.
1. (a) Suppose an object is moving along a straight line, find its instantaneous velocity as a function
of time during the time period 0 ≤ 𝑡 ≤ 4, if its position 𝑥(𝑡) during the same period is given by:
𝑥(𝑡) = 3𝑡 2 − 2𝑡
Answer:
1. (b) Find the average velocity of the same objects above during the same time period 0 ≤ 𝑡 ≤ 4.
Answer:
1
Repeat this question with a different position function: 𝑥(𝑡) = 5 cos (3 𝜋𝑡) after class.
2.
(a) Suppose an object is moving along a straight line, find its displacement between 𝑡 = 0 and
𝑡 = 3 if its instantaneous velocity 𝑣(𝑡) during the time period 0 ≤ 𝑡 ≤ 3 is given by:
v(𝑡) = 𝑡 + 6
2. (b) Find the position of the same objects above as a function of time during the time period 0 ≤
𝑡 ≤ 3, if the object is at position 𝑥 = 2 when 𝑡 = 0.
Repeat this question with a different velocity function: . 𝑣(𝑡) = 7 sin(𝜋𝑡) after class.