An object moves with a velocity of 2 m/s for 5 s, and then its velocity increases uniformly to 10 m/s in next 5 s. Thereafter, its velocity begins to decrease at a uniform rate until it comes to rest after further 5 s. (a) Plot a velocity-time graph for the motion of the object. (b) From the graph, find the total distance covered by the object after 2 s and after 12 s.
Answers
Explanation:
Hint: From the data we first need to draw the v-t graph and d-t graph. Then we need to use the laws of kinematics for uniform acceleration. We have to apply appropriate formulas for different cases and find out what is required. So let us start with the solutions.
Formula used: v=u+at,s=ut+12at2" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: 400; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 46, 43); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">v=u+at,s=ut+12at2v=u+at,s=ut+12at2
Complete answer:
For the first 5s the velocity does not change with time, so the v-t graph will be parallel to the time axis and the d-t graph will be a straight line passing through the origin. Then its velocity increases uniformly for next 5s. Thus its v-t graph will be a straight line and d-t graph will be a curved line with tangent at each point giving the value of the velocity at that time. In the last 10s the velocity decreases uniformly and at last becomes zero. So the v-t graph will be a straight line with negative slope and the d-t graph will also be a curved line with negative slope.
The graphs are shown below.