Question

The velocity-time graph shown below represents the motion of a bodya) During which interval of time, the body is moving with uniform acceleration?b) Calculate the average velocity for the entire journey.

Q. The velocity-time graph shown below represents the motion of a body
a) During which interval of time, the body is moving with uniform acceleration?
b) Calculate the average velocity for the entire journey.

Answer 1

Answer:

Explanation:(i) In the interval of time 0 - 10 sec (OA) acceleration a = (v - u)/t

= (4 - 0)/10 = 0.4 m/s^2

In the interval of time 10 - 20 sec (AB) acceleration a = (v - u)/t

=  5 - 4/20 - 10= 1/10 = 0.1 m/s^2

In the interval of time 20 - 30 sec (BC) acceleration a = (v - u)/t = 7 - 5/30 - 20 = 2/10 = 0.2 m/s^2.

In the interval of time 0 - 10 sec (OA) acceleration is maximum.

or In the 0 - 10 interval of time slop is maximum so at this interval of time acceleration is maximum.

(ii) Distance travelled by body = area of triangle + area of trap 1 + area of trap 2 = 1/2 x 10 x 4 + 1/2 (5 + 4) x 10 + 1/2 (7 + 5) x 10

= 1/2(40 + 90 + 120) = 250/2 = 125 m

Total time = 30 sec.

Average velocity = Total distance/Total time = 125/30 = 4.17 m/s