Advanced: A car starts from rest and accelerates at a rate of 3 m/s² for 8 seconds. What is its final velocity?
Answer: Final velocity = Initial velocity + (acceleration × time)
Advanced: A train decelerates uniformly from 30 m/s to rest in 20 seconds. What is its deceleration rate?
Answer: Use the formula: Acceleration = Change in velocity / Time
Advanced: A ball is thrown vertically upward with an initial velocity of 25 m/s. Calculate the time it takes to reach its maximum height.
Answer: Use kinematic equations to find time to reach maximum height.
Advanced: An object is thrown horizontally from a height of 40 meters with a velocity of 15 m/s. How long does it take to reach the ground?
Answer: Use the equation: H = 0.5gt² to solve for time.
Advanced: A cyclist covers the first half of a journey at an average speed of 10 m/s and the second half at an average speed of 15 m/s. Calculate the average speed for the whole journey.
Answer: Average speed = Total distance / Total time
Challenge: A particle moves in a straight line. Its displacement-time equation is s = 2t³ - 3t² + 2t. Calculate its acceleration when t = 2 seconds.
Answer: Calculate the second derivative of displacement with respect to time to find acceleration.
Challenge: A rocket is launched vertically upward from the ground with an initial velocity of 100 m/s. What maximum height does it reach? (Assume g = 9.81 m/s²).
Answer: Use the kinematic equation v² = u² + 2as to solve for displacement.
Challenge: A stone is thrown horizontally from a cliff with a velocity of 20 m/s. How far from the base of the cliff does it land if the cliff height is 30 meters?
Answer: Use horizontal motion equations to determine time taken to reach the ground and calculate horizontal distance traveled.