Examples:

a. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels?

Solution:

Given: vi = 0 m/s vf = 44 m/s t = 1.80 s

Find: a = ?? d = ??

a = (Delta v)/t

a = (444 m/s - 0 m/s)/(1.80 s)

a = 247 m/s²

d = v_i*t + 0.5*a*t²

d = (0 m/s)*(1.80 s)+ 0.5*(247 m/s²)*(1.80 s)²

d = 0 m + 400 m

d = 400 m

(Note: the d can also be calculated using the equation v_f² = v_i² + 2*a*d)

b. An airplane accelerates down a runway at 3.20 m/s² for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.

Solution:

Given: a = +3.2 m/s2 t = 32.8 s vi = 0 m/s

Find: d = ??

d = v_i*t + 0.5*a*t²

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s²)*(32.8 s)²

d = 1720 m

c. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?

Solution:

Given: a = -9.8 m t = 2.6 s vi = 0 m/s

Find: d = ?? vf = ??

d = v_i*t + 0.5*a*t²

d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s²)*(2.6 s)²

d = -33 m (- indicates direction)

v_f = v_i + a*t

v_f = 0 + (-9.8 m/s²)*(2.6 s)

v_f = -25.5 m/s (- indicates direction)