Physics 101 Sample Problems with Solutions - Kinematics

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1. 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.
   

   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
2. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.
   

   Given: vi = 18.5 m/s vf = 46.1 m/s t = 2.47 s

   Find: d = ?? a = ??

   a = (Delta v)/t
   a = (46.1 m/s - 18.5 m/s)/(2.47 s)
   a = 11.2 m/s²
   d = v_i*t + 0.5*a*t²
   d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s²)*(2.47 s)²
   d = 45.7 m + 34.1 m
   d = 79.8 m
   (Note: the d can also be calculated using the equation v_f² = v_i² + 2*a*d)
3. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s². Determine the time for the feather to fall to the surface of the moon.
   

   Given: vi = 0 m/s d = -1.40 m a = -1.67 m/s2

   Find: t = ??

   d = v_i*t + 0.5*a*t²
   -1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s²)*(t)²
   -1.40 m = 0+ (-0.835 m/s²)*(t)²
   (-1.40 m)/(-0.835 m/s²) = t²
   1.68 s² = t²
   t = 1.29 s
4. A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo.
   

   Given: a = -9.8 m/s2 vf = 0 m/s d = 2.62 m

   Find: vi = ??

   v_f² = v_i² + 2*a*d
   (0 m/s)² = v_i² + 2*(-9.8 m/s²)*(2.62 m)
   0 m²/s² = v_i² - 51.35 m²/s²
   51.35 m²/s² = v_i²
   v_i = 7.17 m/s
5. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)?
   

   Given: a = -9.8 m/s2 vf = 0 m/s d = 1.29 m

   Find: vi = ?? t = ??

   v_f² = v_i² + 2*a*d
   (0 m/s)² = v_i² + 2*(-9.8 m/s²)*(1.29 m)
   0 m²/s² = v_i² - 25.28 m²/s²
   25.28 m²/s² = v_i²
   v_i = 5.03 m/s
   To find hang time, find the time to the peak and then double it.
   v_f = v_i + a*t
   0 m/s = 5.03 m/s + (-9.8 m/s²)*t_up
   -5.03 m/s = (-9.8 m/s²)*t_up
   (-5.03 m/s)/(-9.8 m/s²) = t_up
   t_up = 0.513 s
   hang time = 1.03 s