Question

the velocity time graphs of two objects make angles of 30 and 60 degree's with the time axis find the ratio of their acceleration

Answer 1

Problem:

The velocity time graphs of two objects make angles of 30 and 60 degree's with the time axis find the ratio of their acceleration.

Solution:

Acceleration is defined by the formula:

$$a = \frac {d v}{d t} = \frac {\Delta v}{\Delta t}$$

This value can be calculated as the tangens(tan) function of the velocity time graph angle:

$$a = \tan (\alpha)$$

Thus, the acceleration of this two objects is

$$a _ {1} = \tan (\alpha_ {1}) = \tan \left(\frac {\pi}{6}\right) = 1 / \sqrt {3}$$ $$a _ {2} = \tan (\alpha_ {2}) = \tan \left(\frac {\pi}{3}\right) = \sqrt {3}$$

If in given graph velocity is defined in $m/s$ units, then acceleration calculated above has units $\frac{m}{s^2}$ accordingly.

Answer: $a_1 = 1 / \sqrt{3}, a_2 = \sqrt{3}$ .