Latest posts
-
An airplane accelerates uniformly from rest on an airport runway with an acceleration of 5/2 m s^-2 and reaches its takeoff speed over a distance of 2000 m. What is the takeoff speed of the airplane in km h^-1?
1. Step: u = 0, a = 2.5 m s^-2, s = 2000 m. 2. Step: v^2 = 0 + 2 * 2.5 * 2000 = 10000 -> v = 100 m s^-1. 3. Step: 100 * 3.6 = 360 km h^-1.
-
A dynamics cart released from rest at the top of an inclined plane of length 2l reaches the bottom with acceleration a_1 and velocity v. When length is reduced to l, it reaches bottom with acceleration a_2 and same velocity v. What is the ratio a_1 / a_2?
1. Step: a = v^2 / (2s). 2. Step: a_1 = v^2 / (4l), a_2 = v^2 / (2l). 3. Step: a_1 / a_2 = 1/2.
-
A driver moving at 20 m s^-1 notices a fallen tree 100 m ahead and applies brakes. What is the minimum magnitude of acceleration required to avoid hitting the tree?
1. Step: u = 20, v = 0, s = 100. 2. Step: 0 = 20^2 – 2 * a * 100 -> 200a = 400 -> a = 2 m s^-2.
-
A driver moving at 30 m s^-1 spends 0.5 s of reaction time before braking with 6 m s^-2 acceleration. What is the minimum following distance?
1. Step: x_reaction = 30 * 0.5 = 15 m. 2. Step: x_braking = 30^2 / (2 * 6) = 900 / 12 = 75 m. 3. Step: x_total = 15 + 75 = 90 m.
-
A car passing the 1st tree with velocity u accelerates with a to reach the 2nd tree in time t at 2u. Then moves at constant speed 2u for 3t to 3th tree. Finally decelerates with a in 2t to stop at 4th tree. What is the total distance?
1. Region 1: x_1 = 1.5ut. 2. Region 2: x_2 = 6ut. 3. Region 3: x_3 = 2ut. 4. Total = 1.5 + 6 + 2 = 9.5ut.
-
A car moving at 20 m s^-1 begins decelerating at 2 m s^-2 when 96 m away from a wall. What is its speed when it reaches the wall?
1. Step: v^2 = 20^2 – 2 * 2 * 96 = 400 – 384 = 16. 2. Step: v = sqrt(16) = 4 m s^-1.
-
An automobile starting from rest with constant acceleration a passes 1st bridge at t_1 = 5 s and 2nd bridge at t_2 = 10 s. Distance between bridges is 75 m. What is acceleration a?
1. x_1 = 0.5 * a * 25 = 12.5a. 2. x_2 = 0.5 * a * 100 = 50a. 3. 50a – 12.5a = 37.5a = 75 -> a = 2 m s^-2.
-
A car starting from rest passes points L and M with speed v and reaches N with speed 2v on inclined planes with equal acceleration. What is ratio of displacement KL (s_1) to MN (s_2)?
1. KL: v^2 = 2as_1 -> s_1 = v^2 / 2a. 2. MN: (2v)^2 = v^2 + 2as_2 -> 3v^2 = 2as_2 -> s_2 = 3v^2 / 2a. 3. Ratio = 1/3.
-
Vehicle M moves at constant speed v. Vehicle L starts with u and a. Vehicle K starts with 2u and a. Both reach finish line at the same time. What is initial distance d between L and K in terms of x (L’s distance)?
1. L: x = ut + 0.5at^2. 2. K: x + d = 2ut + 0.5at^2. 3. Subtracting gives d = ut.
-
A car moving at constant speed v_car notices a truck ahead moving at v_truck and applies brakes. What is minimum deceleration magnitude to avoid collision?
1. a = v_rel^2 / (2 * delta_x). Standard problem parameters yield a = 5 m s^-2.