Question

The state of illinois cycle rider safety program requires motorcycle riders to be able to brake from 30 mph (44 feet/second) to zero in 45 feet. what constant deceleration is required to do that?

Answer 1

21.5 ft/s^2 The formula for distance traveled under constant acceleration is d = 0.5 AT^2 where d = distance A = acceleration T = time Solving for A, gives d = 0.5 AT^2 2d = AT^2 (1) 2d/T^2 = A The formula for velocity under constant acceleration is V = AT Solving for A, gives V = AT (2) V/T = A Now setting equations (1) and (2) above equal to each other and solving for T: V/T = 2d/T^2 TV = 2d (3) T = 2d/V Now substitute equation (3) into (2) above. V/T = A V/(2d/V) = A V * V/2d = A V^2/2d = A Plug in values and calculate. V^2/2d = A (44 ft/s)^2/(2*45 ft) = A (1936 ft^2/s^2)/(90 ft) = A 21.51111111 ft/s^2 = A Rounding to 3 significant figures gives 21.5 ft/s^2