Frame of reference; motion in a straight line; uniform and non-uniform motion; scalars and vectors; vector addition and subtraction; motion in a plane; projectile motion; uniform circular motion.
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Q1 · Kinematics · EASY
A particle moves along a straight line such that its displacement x (in metres) at time t (in seconds) is given by x = 4t² + 2t + 1. What is the velocity of the particle at t = 2 s?
Q2 · Kinematics · MEDIUM
A projectile is thrown from the ground at an angle of 30° with the horizontal with an initial velocity of 40 m/s. What is the maximum height reached by the projectile? (Take g = 10 m/s²)
Q3 · Kinematics · EASY
Two vectors A and B have magnitudes 3 units and 4 units respectively. The angle between them is 60°. What is the magnitude of their resultant vector?
Q4 · Kinematics · MEDIUM
A particle is moving in a circle of radius 5 m with a constant speed of 10 m/s. What is the magnitude of the change in velocity when the particle moves through an angle of 60°?
Q5 · Kinematics · HARD
A projectile is fired at an angle θ with the horizontal from the top of a tower of height 60 m with an initial speed of 30 m/s. If the horizontal range is equal to the height of the tower, what is the value of tan θ? (Take g = 10 m/s²)