the displacement-time graph of two bodies P and Q are straight lines making angles 30° and 60° respectively with time axis .Calculate the ratio of velocities P and Q
To calculate the ratio of velocities between bodies P and Q, we need to analyze the displacement-time graphs of both bodies.
Let's denote the displacement of body P at a given time t as DP(t), and the displacement of body Q at the same time t as DQ(t). Since both graphs are straight lines, we can determine the equation of each line using the slope-intercept form, y = mx + b.
For body P, the angle it makes with the time axis is 30°. The slope (m) of the line can be determined using the tangent of the angle:
mP = tan(30°) = 1/√3.
For body Q, the angle it makes with the time axis is 60°. Again, we can calculate the slope (m) using the tangent of the angle:
mQ = tan(60°) = √3.
Now, let's assume the ratio of velocities between P and Q is vP:vQ. The ratio of velocities is the same as the ratio of the slopes:
vP/vQ = mP/mQ = (1/√3)/(√3) = 1/3.
Therefore, the ratio of velocities between bodies P and Q is 1:3.
Remember, to determine the slopes of the displacement-time graphs, you need to use the angles they make with the time axis, and calculate the tangents of those angles.