Unit 1: Kinematics Test

1. A car starts from rest and accelerates at 3 m/s² for 8 s. Find final velocity and displacement.
2. A projectile is launched at 20 m/s at 30° above horizontal. Find max height, range, and flight time.
3. Two vectors: \(A = 5 \hat{i} + 12 \hat{j}\), \(B = -9 \hat{i} + 4 \hat{j}\). Find \(A+B\) and its magnitude and direction.
4. A boat moves 50 m north, then 120 m east. Find resultant displacement and angle.
5. Velocity components of a particle: \(v_x = 6\) m/s, \(v_y = -8\) m/s. Find speed and direction.
6. A ball rolls off a 2.5 m high table with horizontal velocity 3 m/s. Determine time of flight and horizontal displacement.
7. Relative motion: Plane flies east at 100 m/s; wind blows north at 20 m/s. Find velocity relative to ground.
8. A particle moves along x-axis: \(x = 2t^2 - 4t\). Find acceleration and velocity at t = 3 s.
9. A vector has magnitude 15 N at 45° above horizontal. Find components along x and y.
10. A train moves with uniform acceleration from 10 m/s to 30 m/s in 20 s. Find acceleration and distance traveled.