Lab 4 Kinematics in One-Dimension

Data Tables: Tabla 1. Data Table Dot Time (s) Displacement (cm) Displacement Δx (m) Sparker time interval 2Δt (s) Velocity (m/s) Acceleration m/s² 1 0,50 5 0,05 0,20 0,250 2 1,00 6,4 0,064 0,20 0,320 0,14 3 1,50 8,2 0,082 0,20 0,410 0,18 4 2,00 10,3 0,103 0,20 0,515 0,21 5 2,50 12,3 0,123 0,20 0,615 0,20 6 3,00 13,9 0,139 0,20 0,695 0,16 7 3,50 15,6 0,156 0,20 0,780 0,17 8 4,00 17,3 0,173 0,20 0,865 0,17 9 4,50 18,9 0,189 0,20 0,945 0,16 10 5,00 20,5 0,205 0,20 1,025 0,16 Calculations: Δ t is constant and equal to 0.1 s for each interval, the calculation for each time interval will involve dividing the change in displacement Δ x between each pair of consecutive points by 2 Δ t = 2 * 0.1 s . = 0.20 s Velocity : Now we calculate the average velocity for each interval by dividing  For t = 0.5 s, v = 0.050 / 0.20 = 0.250 m/s  For t = 1.0 s, v = 0.064 / 0.20 = 0.320 m/s 3

If the velocity at t = 0.5 s is v = 0.25 m / s and the velocity at t = 1.0 s is v = 0.32 m / s , then the acceleration over that time interval: a = ( 0.32 m/s – 0.25 m/s) / ( 1.0 s – 0.5 s ) = 0.07 m/s / 0.5 s = 0.14 m/s² Discussion: The experiment conducted in Laboratory #4 focused on studying the motion of a cart moving on an air track. From the gathered data, a Velocity vs. Time Graph (Graph 1) was generated, displaying a clear linear trend. This behavior is characteristic of uniformly accelerated motion, aligning with the theoretical principles discussed in the lectures. From the slope of Graph 1 , an average acceleration of 0.17 m/s² was determined. This acceleration aligns with the data presented in Table 1 . However, variations in acceleration values were noted, fluctuating between 0.14 m/s² and 0.21 m/s² throughout the experiment. Such fluctuations could be attributed to factors such as potential imperfections on the air track, misalignments of the cart, or variations in the operation of the spark timer. A significant point of interest was the displacement of the cart between t=1.5s and t=3.5s. Using the trapezoid formula to compute the displacement, a value of 1.361 m was derived. However, when directly measuring from the spark tape, a displacement of 1.36 m was recorded. Despite the minimal difference of 0.001 m between these values, it underscores the precision of the technique and the importance of employing diverse methods for result verification. The velocity relationship was described by the equation v ( t ) = 0.250 m / s + 0.1722 m / s² × t , emphasizing how velocity varies over time under constant acceleration. In kinematic theory, it is said that an object should start from rest, but in reality, this rarely happens. In Table 1 , an initial velocity of 0.250 m/s is observed for the cart, 6