Section 1.9: Mixed Practice (Kinematics)

This section combines concepts from previous sections (1.1–1.8). Problems include one-dimensional motion, relative velocity, graphical analysis, and problem-solving strategies.

Mixed Practice Problems

  1. A car accelerates from rest at 2 m/s² for 10 s. Find final velocity and displacement.
  2. A boat moves at 5 m/s relative to water, and the river flows at 3 m/s. Find the boat's velocity relative to the shore if it moves upstream and downstream.
  3. A runner travels 100 m in 12 s, then continues at 4 m/s for another 10 s. Find total distance and average speed.
  4. A car decelerates from 30 m/s to rest in 15 s. Find acceleration and stopping distance.
  5. A projectile is launched at an angle of 30° with speed 20 m/s. Calculate horizontal and vertical components of velocity at launch.
  6. A particle moves according to v = 2t + 3 m/s. Find displacement in 5 s using integration/area under graph.
  7. An object moves 50 m with constant acceleration 2 m/s² starting from rest. Find time and final velocity.
  8. A train moving at 20 m/s accelerates at 1 m/s² for 10 s. Find distance covered and final velocity.
  9. A cyclist slows down from 15 m/s to 5 m/s over 20 m. Find deceleration and time.
  10. A car accelerates from 5 m/s to 15 m/s over 100 m. Use appropriate kinematic equation to find time and acceleration.
  11. A runner accelerates from 0 to 12 m/s in 8 s, then maintains constant velocity for 10 s. Find total displacement.
  12. An object is projected horizontally from a height of 10 m with speed 5 m/s. Find time to hit the ground and horizontal distance.
  13. A boat moves perpendicular to a river flowing at 4 m/s. Boat speed relative to water is 3 m/s. Find resultant velocity and direction.
  14. From a velocity-time graph: a car accelerates uniformly from 0 to 20 m/s in 10 s. Find distance using area under graph.
  15. A particle moves along a line with velocity v = 4t – 2. Find displacement after 6 s.
  16. A car decelerates from 25 m/s to 10 m/s over 60 m. Find acceleration and time.
  17. A motorcycle moves 100 m in 8 s from rest with uniform acceleration. Find final velocity and acceleration.
  18. A train starts from rest and accelerates at 0.5 m/s² for 120 s. Find final velocity and distance.
  19. A runner starts from 3 m/s and accelerates at 2 m/s² for 6 s. Find final speed and displacement.
  20. A particle is moving with velocity v = 5 – 0.5t m/s. Find displacement after 8 s.
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