Question

The v-t graph of a moving body is given below. The distance covered by the body in

the first 40s is _________and its acceleration during the last 40s is _____________.


a) 3200m; 2ms-1

b) 700m; -2ms-2

c) 900m; - 2ms-2

d) 900m; 2ms-2​

Answer 1

Answer: The correct answer is a) 3200 m,
`-2m/s^2`

Step-by-step explanation:

Speed is defined as the ratio of distance travelled to the time taken. The equation follows:

`\text{Speed}=\frac{\text{Distance travalled}}{\text{Time taken}}`

From the graph:

Speed for the first 40 s, v = 80 m/s

Time taken, t = 40 s

Putting values in above equation, we get:

`\text{Distance travalled}=(80 m/s* 40s)=3200 m`

Acceleration is defined as the ratio of change of velocity to the change of time. The equation follows:

`\text{Acceleration}=(\Delta v)/(\Delta t)=(v_2-v_1)/(t_2-t_1)`

From the graph, for the last 40 sec:

Initial velocity,
`v_1` = 80 m/s

Final velocity,
`v_2` = 0 m/s

Initial time,
`t_1` = 40 s

Final time,
`t_2` = 80 s

Putting values in above equation, we get:

`\text{Acceleration}=((0-80)m/s)/((80-40)s)\\\\\text{Acceleration}=(-80m/s)/(40s)=-2m/s^2`

Hence, the correct answer is a) 3200 m,
`-2m/s^2`