Question

An object moves at a slow, constant v speed, then sits at rest for a moment, then moves at a new faster, constant speed. Sketch a velocity-time graph of this motion on the given axes.

Answer 1

Given:

An object moves with a constant speed "v", rests for a moment and then moves at new speed (faster than before).

Required answer:

To draw a velocity-time graph for the above given motion.

Explanation:

Speed: Speed is defined as the distance travelled by an(a) object/ item/thing in a given time.

• It is given by the formula: $Speed=Distance/Time$
• Constant speed is the term used when the rate of change of distance between consecutive points is similar. This can be explained using the equation as follows:

Constant Speed ⇒$(d_1-d_2)/(t_1-t_2) = (d_2-d_3)/(t_2-t_3)$

Velocity: Velocity is defined as the displacement covered by an object in a given time.

• Displacement is defined as the shortest distance between two points.
• Velocity is given by the formula: $Velocity = Displacement/ Time$

However, both the speed and velocity are considered the same, in practice.

The area under Velocity - Time / Speed - Time graph gives the "Acceleration" or "Deceleration".

Answer:

• From the given data, at first the object moves with constant speed "v" for a certain time(say "t₁"). The graph of constant speed is a horizontal line. This is shown as a straight line in 1st spell in the image attached.
• To come to rest, the object experiences decrement in its speed, which is termed as "Deceleration".
• Later, the object is at rest. This means that the speed of object is reduced to "zero" for a certain time (say "t₂"). This part is shown with the term "Rest".
• Now, after rest, to attain the required constant speed, the object experiences an increment in speed from zero to the required speed. This is termed as "Acceleration".
• After rest, the objects starts with higher speed than before. And, again it moves with constant speed. This is shown as the 2nd spell with a horizontal line in the image.

Note: An image is attached showing the velocity-time graph for the given motion.