The magnitude of the acceleration for the speeding up phase is
*
The magnitude of the acceleration for the slowing down phase is
*

Further explanation

From the v-t graph, we see that:

the object at rest at time interval 0 ≤ t the object is speeding up and slowing down at interval 0.20

In physics, acceleration is the rate of change of velocity per unit time.

You are watching: Determine the magnitude of the acceleration for the speeding up phase.

*

In mathematics, acceleration is the gradient or slope of the line with the vertical axis is velocity (v) and the horizontal axis is time (t).

Remember this,

*

The same analogy for the acceleration formula, i.e.

*

The two points that cause the upward-sloping line are

*

*

*

*

We get the magnitude of the acceleration for the speeding up phase is

*

The two points that cause the downward-sloping line are

*

*

*

*

We get the magnitude of the acceleration for the speeding up phase is

*
with a negative sign.

Note:

Positive slope, in other words speeding up, produces a positive sign of acceleration. The acceleration is in a similar direction as the velocity. Example: free-falling object.Negative slope, in other words slowing down, produces a negative sign of acceleration. The acceleration is precisely in the opposite direction as the velocity. Example: the car is slowing or braking.Acceleration is precisely a vector quantity defined as the rate at which an object changes its velocity.

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Keywords: determine, the magnitude, acceleration, speeding up, slowing down, phase, time interval, at rest, the rate, change, velocity, unit, upward, downward, sloping lines, gradient


*

*

The magnitude of the acceleration for speeding up phase is

*
and for slowing down phase is
*

Further explanation

Acceleration can be stated as the rate of change of velocity with respect to time in a specified direction. It is denoted as

*

Velocity can be stated as the rate of change of distance with respect to time in a specified direction. It is denoted as

*
.

Both the terms are vector quantity.

The magnitude of the acceleration can be calculated as,

*

Here,

*
are the velocities at the time
*
respectively.

Step 1:

The horizontal axis represents time and vertical axis represents

It can be seen from the given graph that the object is on the rest at time interval

*
and
*
.

It can be observed from the given graph the velocity function is rising in the interval of time

*
.

The velocity of the object at time

*
is
*
and the velocity of the object at time
*
is
*
.

Therefore, the values of

*
can be written as,

*

Substitute the value of

*
in the formula of acceleration to find the value of acceleration as,

*

The magnitude of the acceleration for the speeding up phase is

*
.

Step 2:

It can be observed from the given graph the velocity function is declining in the interval of time

*
.

The velocity of the object at time

*
is
*
and the velocity of the object at time
*
is
*
.

Therefore, the values of

*
can be written as,

*

Substitute the value of

*
in the formula of acceleration to find the value of acceleration as,

*

Here, the magnitude of the acceleration for the slowing down phase is negative.

Note:

Negative slope represents the slowing down phase and it is in the downward direction.

Example: when the car is slowing down its speed or applying brakes.

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Positive slope represents the speeding up phase and it is in the upward direction.

Example: free falling object

Learn more:

medtox.org details:

Grade: Middle school

Subject: Mathematics

Chapter: Speed and distance

Keywords: Speed, velocity, distance, acceleration, vector quantity, slowing down, braking, change, magnitude, unit, upward, slope, time interval