Question

This graph shows the velocity of particles A and B through time. The two lines intersect each other at point O. What is the acceleration of particles A and particle B at point O?

A.
It is -0.2 m/s2 for particle A and -0.05 m/s2 for particle B.
B.
It is 0.65 m/s2 for both particles.
C.
It is 0.68 m/s2 for both particles.
D.
It is -2 m/s2 for particle A and -0.50 m/s2 for particle B.

Answer 1

Option (D)

Step-by-step explanation:

Since acceleration of an object = Change in velocity with the change in time

a =
`(v_2-v_1)/(t_2-t_1)` =
`(\triangle v)/(\triangle t)`

Here
`(v_1,t_1)` and
`(v_2,t_2)` are the two points on the line on the graph.

Therefore, slope of the line will represent the acceleration (constant) at any point lying on the line.

For particle A,

Two points on the line are (0, 2) and (1, 0)

a =
`(2-0)/(0-1)`

`a_1` = -2 meter per sec²

Similarly, for the particle B,

There are two points (0, 1) and (2, 0) on the line.

`a_2` =
`(1-0)/(0-2)` =
`-(1)/(2)`

`a_2=-0.5` meter per sec²

Therefore, at any moment of time acceleration of the particle A will be (-2) meter per sec² and for particle B will be (-0.5) meter per sec².

Option (D) will be the correct option.