Trevon drives with velocity v₁ = (55î ─ 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon's displacement? Write your answer in component form using unit vectors.

Verified step by step guidance

1. Calculate the displacement for each segment of the trip. Displacement is given by the formula \( \vec{d} = \vec{v} \times t \), where \( \vec{v} \) is the velocity vector and \( t \) is the time.
2. For the first segment with velocity \( \vec{v}_1 = (55\hat{i} - 10\hat{j}) \) mph for 1.0 hour, use the displacement formula: \( \vec{d}_1 = \vec{v}_1 \times t_1 = (55\hat{i} - 10\hat{j}) \times 1.0 \).
3. For the second segment with velocity \( \vec{v}_2 = (20\hat{i} + 50\hat{j}) \) mph for 2.0 hours, use the displacement formula: \( \vec{d}_2 = \vec{v}_2 \times t_2 = (20\hat{i} + 50\hat{j}) \times 2.0 \).
4. Add the displacements from each segment to find the total displacement: \( \vec{d}_{total} = \vec{d}_1 + \vec{d}_2 \).
5. Express the total displacement in component form using unit vectors \( \hat{i} \) and \( \hat{j} \).

Key Concepts

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It has both magnitude and direction, which means it is represented in component form using unit vectors. In this question, Trevon's velocities v₁ and v₂ are given in terms of unit vectors, indicating the direction of his movement in a two-dimensional plane.

Displacement

Displacement is the vector quantity that represents the change in position of an object. It is calculated as the final position minus the initial position and is also expressed in component form. In this scenario, Trevon's total displacement will be the vector sum of the displacements during each segment of his journey, taking into account the time and direction of travel.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. This involves adding the corresponding components of the vectors. In this problem, Trevon's total displacement is found by calculating the displacement for each segment of his trip and then adding these vectors together to find the overall change in position.