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**Tip 1:**

- Instantaneous velocity is calculated by taking time derivative of position vector and instantaneous acceleration is calculated by taking derivative of velocity vector with respect to time.

**Practice these problems:-**

Problem solving tips

5 min read

- Want to score better marks in exams? Have a look at some problem solving tips.

1

- Instantaneous velocity is calculated by taking time derivative of position vector and instantaneous acceleration is calculated by taking derivative of velocity vector with respect to time.

2

- For any two motion in 2D resolve the quantities as velocity , acceleration, etc along x axis and along y axis.
- The x part of motion occurs exactly as it would if the y- part did not occur at all. Similarly, y part of motion occurs exactly as it would if the x part of motion did not occur. In other words X and Y motion at independent of each other.
- So solve equations along x axis and along y axis using equation of motion separately.

3

- Write down given information for x and y axis separately.
- If you don't know time, solve for it first because time is same for both direction and will be same for both axis.
- Acceleration due to gravity, i.e, acceleration in Y direction is -9.8 unless specified.
- Acceleration in X direction is zero unless specified.
- In one dimension(X- axis), there is uniform motion, and in other dimension(Y-axis) there is uniform accelerated motion. (Unless specified)

4

- Velocity and acceleration are not in the same direction, velocity points in the direction of motion which is tangent to the circle and acceleration is always directed towards the center. Velocity and acceleration are perpendicular to each other at each point..

5

- First we draw the figure, i.e, the given velocity vectors.
- Remember the time is same for all components of the problem.
- The basic principle in these problems is vector addition or subtraction.
- In boat river problem the boat crosses the river by the shortest path if it moves perpendicular to the river current, the boat takes the shortest time when he swims perpendicular to the river velocity and boat will have minimum drift if boat reaches directly opposite point.
- Flight problems are same as river problems except in air instead of water.