
The gradient or slope of the distance time graph at any point gives
A. Acceleration
B. Distance
C. Velocity
D. Time
Answer
479.7k+ views
Hint: In this question, we need to comment on the result of the gradient or the slope of the distance time graph at any point. For this, we will use the definition of the slope (or gradient) of the curve and try to establish the relation with the given options.
Complete step by step answer:
Slope in distance time graph is given by
$\dfrac{{dx}}{{dt}} = \dfrac{{displacement}}{{time}}$
This is also known as velocity.
Thus the slope of a distance time graph at any point gives the velocity of a particle. It is also known as the displacement per unit time.
Its unit is $m{s^{ - 1}}$ or metre per second.
So, the correct answer is “Option C”.
Additional Information:
Below is the table which shows the quantities represented by the areas and slopes of the different kinematics graphs that is the displacement time graph, velocity time graph and acceleration time graph.
The slope of acceleration time graph and area of distance time graph doesn’t give any quantity.
Note:
The slope or gradient of a graph is given by $\dfrac{{dy}}{{dx}}$ . This means that the quantity in y-axis is divided by the quantity in x-axis to get the slope. Students generally get confused over the areas and slopes of the different graphs in the kinematics chapter. An easy way is to multiply the quantities in x and y axis when asked the area and to divide the quantity in y axis by the quantity in x axis when asked the slope and get an idea of the quantity accordingly.
Complete step by step answer:
Slope in distance time graph is given by
$\dfrac{{dx}}{{dt}} = \dfrac{{displacement}}{{time}}$
This is also known as velocity.
Thus the slope of a distance time graph at any point gives the velocity of a particle. It is also known as the displacement per unit time.
Its unit is $m{s^{ - 1}}$ or metre per second.
So, the correct answer is “Option C”.
Additional Information:
Below is the table which shows the quantities represented by the areas and slopes of the different kinematics graphs that is the displacement time graph, velocity time graph and acceleration time graph.
Graphs | Slope | Area |
Displacement Time graph | Velocity | -- |
Velocity Time graph | Acceleration | Displacement |
Acceleration Time graph | -- | Change in velocity |
The slope of acceleration time graph and area of distance time graph doesn’t give any quantity.
Note:
The slope or gradient of a graph is given by $\dfrac{{dy}}{{dx}}$ . This means that the quantity in y-axis is divided by the quantity in x-axis to get the slope. Students generally get confused over the areas and slopes of the different graphs in the kinematics chapter. An easy way is to multiply the quantities in x and y axis when asked the area and to divide the quantity in y axis by the quantity in x axis when asked the slope and get an idea of the quantity accordingly.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
State and prove Bernoullis theorem class 11 physics CBSE

What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

Why is steel more elastic than rubber class 11 physics CBSE

Explain why a There is no atmosphere on the moon b class 11 physics CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE
