The distance traveled by a particle starting from rest is plotted against the square of the time elapsed from the start of the motion. The graph is a straight line. The gradient of the line is 4.9 m/s². Determine the acceleration of the motion.?
d=vo*t + 1/2 a t^2 and vo=0
letting t^2= u
d= +1/2 a u
so as d is a function of u, then slope is 1/2 a
4.9=1/2 a or a= 9.8 m/s^2
To determine the acceleration of the motion, we can use the equation for the gradient of a straight line, which is given by:
gradient = change in y / change in x
In this case, the gradient of the line represents the acceleration, and the y-axis represents the distance traveled by the particle, while the x-axis represents the square of the time elapsed.
Therefore, the acceleration can be calculated by finding the change in y (distance) divided by the change in x (square of the time elapsed).
Since the gradient of the line is given as 4.9 m/s², it means that for every unit increase in the x-axis (time squared), the distance (y-axis) increases by 4.9 meters per second squared.
Hence, the acceleration of the motion is 4.9 m/s².