Question

A velocity vs. time graph starts at 0 and ends at 10 m/s, stretching over a time- span of 15 s with constant acceleration. What is the object's net displacement? ​

Answer 1

Answer:

75m

Explanation:

Answer 2

The object's net displacement is "75 m".

The straight-line velocity-time graph means the acceleration of the object is constant. For the constant acceleration case, the equations of motion can be used to find out the missing variable, which is the net displacement in this case.

Using the first equation of motion, to find the acceleration first:

$v_f=v_i+at$

where,

vi = initial velocity = 0 m/s

vf = final velocity = 10 m/s

a = consatnt acceleration = ?

t = time = 15 s

This data has been extracted from the graph provided in the attached picture. This graph has been made according to the given conditions in the question.

Using these values in the equation we get:

$10\ m/s = 0\ m/s + a(15\ s)\\\\a = \frac{10\ m/s}{15\ s}\\\\a=0.667\ m/s^2$

Now, we will use the second equation of motion to find out the net displacement:

$s=v_it+\frac{1}{2}at^2$

where,

s = net displacement = ?

Therefore, using the values:

$s = (0\ m/s)(15\ s)+\frac{1}{2}(0.667\ m/s^2)(15\ s)^2$

s = 75 m

Learn more about the equations of motion here:

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