Practice Problems

1. A car accelerates from 0 to 20 m/s in 5 s along a straight road. Find its acceleration and distance traveled.
2. A projectile is launched at 15 m/s at 40° above horizontal. Find max height, range, and flight time.
3. Two vectors: \(A = 8 \hat{i} + 6 \hat{j}\), \(B = -3 \hat{i} + 4 \hat{j}\). Find \(A+B\) and its magnitude and direction.
4. A boat moves across a river 100 m wide with current 3 m/s. Boat speed in still water: 4 m/s. Find heading and displacement downstream.
5. A particle moves with \(x = 3t\), \(y = 4t - 2t^2\). Find velocity and acceleration at t = 2 s.
6. A ball rolls off a 5 m high table at 2 m/s. Find time of flight and horizontal displacement.
7. Relative motion: A plane flies north at 80 m/s; wind blows east at 20 m/s. Determine velocity relative to ground.
8. A vector has magnitude 12 N at 30° above horizontal. Find x and y components.
9. A projectile lands 40 m from the base of a cliff after 2 s. Find initial horizontal velocity.
10. A car moves along x-axis: \(x = 5t^2\). Find acceleration and velocity at t = 3 s.