Question

The distance travelled by the particle in 8 sec is

A. 18m
B. 16m
C. 8m
D. 6m

Answer 1

Hint: At first look at the graph and analyze it, we will see that the car is first accelerating and then decelerating. So calculate the part at first where it is accelerating and then calculate the decelerating part to find the required result.

Complete answer:
The graph that is given is actually a time velocity graph from which we can define many things like distance travelled.
Now, to find the distance travelled by the particle in time t=8 seconds.
We can do that by, using the formula,
\[S=\dfrac{1}{2}\times (4+2)\times 4+\dfrac{1}{2}\times (2+4)\times 2\] , in this formula we are at fist covering the area or the distance where the graph is positive and then we calculated the distance where the graph is negative.
So on solving, we get
\[S=12+6=18m\]

So, the correct answer is “Option A”.

Additional Information:
Velocity of an object is the rate of change of the object’s position with respect to a frame of reference and which is always a function of time.
Accelerating is nothing but a measure of a body’s capacity of gaining velocity with respect to time or we can say that it is the rate of change of velocity with respect to time and it is a vector quantity

Note:
 In the graph we can see that the body is accelerating at first and then slowly it starts to decelerate and then finally comes to a stop. We can find the acceleration of the body from the graph also we can also calculate the time taken to travel a distance from the graph