A uniformly accelerated particle covers 15 m during its 3rd second and 35 m during its 8th second. Find the displacement from t=0 up to the instant when its speed first becomes 25 m s⁻¹.
Physics · Kinematics Part-1 (one dimension) · Motion under constant acceleration
JEE Mains NEET

Question

A uniformly accelerated particle covers 15 m during its 3rd second and 35 m during its 8th second. Find the displacement from t=0 up to the instant when its speed first becomes 25 m s⁻¹.

G1 Physics · Accepted Answer

For the n-th second, sₙ = u + a(2n−1)/2. For n=3: u + 5a/2 = 15. For n=8: u + 15a/2 = 35. Subtracting, 5a = 20 ⇒ a=4 m s⁻². Then u+10=15 ⇒ u=5 m s⁻¹. Speed first becomes 25 m s⁻¹ at 25 = 5 + 4t ⇒ t=5 s. Displacement: s = ut + at²/2 = 5(5)+2(25) = 75 m.