Chapter 1 Test – Motion in One Dimension & Kinematics
This test covers all topics from Chapter 1, including 1D motion, 2D motion concepts, relative velocity, graphs, and advanced kinematics.
1. Conceptual: Explain the difference between distance and displacement. Provide an example where they are not equal.
Distance is the total path traveled (scalar), displacement is the net change in position (vector). For example, walking 10 m east, then 4 m west: distance = 14 m, displacement = 6 m east.
2. Numerical: A car accelerates from rest at 3 m/s² for 8 s. Find its final velocity and displacement.
v = vo + at = 0 + 3*8 = 24 m/s
d = vo*t + 0.5*a*t² = 0 + 0.5*3*64 = 96 m
3. Multiple Choice: An object moves along a straight line with uniform acceleration. Which graph shows velocity vs. time?
A straight line with slope equal to acceleration.
4. Relative Velocity: A boat moves at 5 m/s relative to water. The river flows at 3 m/s. Find the boat's speed relative to the shore if it moves (a) upstream, (b) downstream, (c) perpendicular to flow.
(a) Upstream: 5 - 3 = 2 m/s
(b) Downstream: 5 + 3 = 8 m/s
(c) Perpendicular: √(5² + 3²) ≈ 5.83 m/s
5. Graphical Analysis: The v-t graph of a particle is a straight line with slope -2 m/s² starting at v = 10 m/s. Find the distance covered until it stops.
v = vo + at; 0 = 10 - 2*t ⇒ t = 5 s
Distance = area under v-t graph = 0.5*(10 + 0)*5 = 25 m
6. Mixed Problem: A particle moves with vo = 4 m/s and accelerates at 2 m/s² for 6 s. Find final velocity and displacement.
v = 4 + 2*6 = 16 m/s
d = 4*6 + 0.5*2*36 = 24 + 36 = 60 m