At what time(s) do the rockets have the same velocity?

Two toy rockets are traveling in the same direction (taken to bethe x axis). A diagram is shown of a time-exposure imagewhere a stroboscope has illuminated the rockets at the uniform timeintervals indicated.

At what time(s) do the rockets have the samevelocity?
at time t=1 only
at time t=4 only
at times t=1 and t=4
at some instant in time between t=1 andt=4
at no time shown in the figure
At what time(s) do the two rockets have thesame acceleration?
at time t=1 only
at time t=4 only
at times t=1 and t=4
at some instant in time between t=1 andt=4
at no time shown in the figure
The motion of the rocket labeled A is anexample of motion with uniform (i.e., constant) __________.
and nonzero acceleration
velocity
displacement
time
The motion of the rocket labeled B is anexample of motion with uniform (i.e., constant) __________.
and nonzero acceleration
velocity
displacement
time
At what time(s) is rocket A ahead of rocketB?
before T=1 only
after T=4 only
before T=1 and after T=4
between T=1 and T=4
at no time(s) shown in the figure

Answer

General guidance

Concept and Reason

The required concepts to solve this question are uniform velocity, and average velocity.

Use the given diagram to compare the displacements, velocity, and acceleration of the both situations.

Fundamentals

The average velocity is defined as the ratio of the distance travelled by the body to the time elapsed. It is a vector quantity

The expression to find out the average velocity of an object is given as follows:

change in position
change in time
*-*
ht
Ax

The expression to find out that the motion is in uniform velocity is given as follows:

to

The acceleration of an object is defined as the rate of change of velocity. It is also a vector quantity.

The expression to find out the acceleration of an object is given as follows:

a_change in velocity
change in time
- - -
12-4

The uniform motion of a body is defined as the motion in which body covers equal distance in equal interval of time. On the other hand, if the body covers unequal distance in equal distance of time.

An object is said to be in uniform velocity when the speed and the direction of the object are not changing with respect to time.

An object is said to be in constant acceleration when the velocity of an object is not changing with respect to time.

The time at which object A is ahead of object B is calculated by looking at the given diagram and find out the time at which object A is to the right of object B.

Step-by-step

Step 1 of 5

(a)

Observe the position of the Rocket A and B and find the time at which the value is same for both the rocket.

The position of the rocket A and B is different for , and whereas the position is same for.

The change in the position for time period and, is approximately the same which gives the time interval at which both the rocket have same velocity.

Part a

The rockets have the same velocity at some instant between and.


The change in the position for time period and, is approximately the same which gives the time interval at which both the rocket has same velocity.

Step 2 of 5

(b)

Observe the position of rocket A and B to find out the time at which both have the same position.

The acceleration is related to how much the velocity changes from one time interval to next. The velocity change is related to the spacing between the images in the given diagram.

Since, the rocket B covers equal distance at equal interval of time implies that the acceleration is zero for rocket B whereas for rocket A acceleration is greater than zero.

For rocket A:

For rocket B:

Hence, there is no time at which both the rockets have same acceleration.

Part b

The two rockets have the same acceleration at no time shown in figure.


Since, the rocket B covers equal distance at equal interval of time implies that the acceleration is zero for rocket B whereas for rocket A acceleration is greater than zero.

Step 3 of 5

(c)

The rocket A covers unequal distances for different time intervals.

For rocket A:

Part c

The motion of rocket A is an example of motion with uniform and non-zero acceleration.


The rocket A covers unequal distances for different time intervals.

The acceleration is related to how much the spacing between the position changes from one time interval to next and that is positive for rocket A.

Step 4 of 5

[Hint for the next step]

Refer the given figure to find the distances with respect to time.

(d)

From the given figure, it is very clear the velocity is always constant with respect to time.

Therefore, B is the example for uniform velocity.

Part d

The motion of rocket B is an example of motion with uniform velocity.


The rocket B covers equal distances for equal time intervals as shown in the figure implies that the object moves with uniform velocity.

Step 5 of 5

(e)

The time at which object A is ahead of object B is calculated by using figure and find out the time at which object A is to the right of object B.

Hence, the time at which rocket A is ahead of rocket B is before and after .

Part e

The time at which rocket A is ahead of rocket B is before and after .


The time at which object A is ahead of object B is calculated by using figure and find out the time at which rocket A is to the right of rocket B.

Answer

Part a

The rockets have the same velocity at some instant between and.

Part b

The two rockets have the same acceleration at no time shown in figure.

Part c

The motion of rocket A is an example of motion with uniform and non-zero acceleration.

Part d

The motion of rocket B is an example of motion with uniform velocity.

Part e

The time at which rocket A is ahead of rocket B is before and after .

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