Question

A velocity vs time graph is a graph that shows the relationship between the velocity of an object over time. is plotted on the x-axis in seconds, and the of the object is plotted on the y-axis in meters per second.

Answer 1

A graph shows a relationship between two variables: independent and dependent. The dependent variable is in the y-axis, while the independent variable is in the x-axis. When it says, plot velocity against time, that means that velocity is in the y-axis in meters per second, and time is in the x-axis in seconds. 

An example of a velocity vs time graph is shown in the attached picture. In this example, the motion is in constant acceleration. This is because it is linear, thereby, the slope is constant. If you want to find the instantaneous velocity at a certain time, create a vertical line from the x-axis until it reaches the diagonal line. Then, draw a horizontal line towards the y-axis to know the value of the velocity.

Answer 2

The velocity graph (v) with respect to time (t) (v on the y axis and t on the x axis) on  :

constant velocity motion shows a straight line parallel to the x-axis (= time)

uniformly accelerated motion shows a sloping straight line with gradient tan θ = a

Further explanation

Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration

• At constant velocity motion:

the speed of vo = v = constant

acceleration = a = 0

Δx = vt or x = xo + vt

An equation of constant velocity motion

$\large {\boxed {\bold {S = v \times \: t}}}$

x = distance = m

v = speed = m / s

t = time = seconds

The velocity graph (v) versus time (t) (v on the y axis and t on the x axis) shows a straight line parallel to the x axis (= time) because it has a constant speed

While the displacement of objects (Δx) is the area under the v-t line

• An equation of uniformly accelerated motion

$\large {\boxed {\bold {x = xo + vo.t + \frac {1} {2} at ^ 2}}}$

V = vo + at

Vt² = vo² + 2a (x-xo)

x = distance on t

vo/vi = initial speed

vt/vf = speed on t /final speed

a = acceleration

Acceleration is a change in speed within a certain time interval

a = Δv /Δ t

$\displaystyle a=\frac{v2-v1}{t2-t1}$

The velocity graph with respect to time (v-t) in this motion will be in the form of sloping straight lines with a gradient of tan θ= a

For acceleration that is positive (a> 0) called accelerated motion, the graph is sloping upward, while for acceleration that is negative (a <0) called slowed down motion , the graph is sloping downward

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Keywords: constant velocity motion, uniformly accelerated motion, v-t graph, distance, speed, acceleration, straight lines