Question

Please answer quickly !! Q. The motion of the body is represented by the following velocity-time graph. What will be the displacement of the body in the first 5s? a) 25m b) 12.5m c) 37.5m d)4om

Answer 1

Given :

▪ Initial velocity = 5mps

▪ Final velocity = 10mps

▪ Time interval = 5s

To Find :

▪ Displacement of the body in first 5s.

Concept :

↗ As per the given velocity vs time graph, we can say that acceleration of the moving body remains same throughout the motion. (Slope of velocity vs time graph gives acceleration.)

↗ We can easily apply equation of kinematics to solve this question. (constant acceleration)

Calculation :

$\dashrightarrow\sf\:v^2-u^2=2as\\ \\ \dashrightarrow\sf\:v^2-u^2=2{\huge{(}}\dfrac{v-u}{t}{\huge{)}}s\\ \\ \dashrightarrow\sf\:(10)^2-(5)^2=2\times \dfrac{10-5}{5}\times s\\ \\ \dashrightarrow\sf\:100-25=2s\\ \\ \dashrightarrow\sf\:s=\dfrac{75}{2}\\ \\ \dashrightarrow\underline{\boxed{\bf{\blue{s=37.5\:m}}}}\:\orange{\bigstar}$

Answer 2

✴ Given :

▪ A velocity vs time graph of the moving body has been provided.

✴ To Find :

▪ Displacement of the body in first 5s.

✴ Calculation :

⭐ Displacement travelled = Area between the (v - t) graph and time axis.

$\rightarrowtail\sf\:d=ABE+BCDE\\ \\ \rightarrowtail\sf\:d=\dfrac{1}{2}(BE\times AB) + (ED\times DC)\\ \\ \rightarrowtail\sf\:d=\dfrac{1}{2}(5\times 5)+(5\times 5)\\ \\ \rightarrowtail\sf\:d=12.5+25\\ \\ \rightarrowtail\bf\:d=37.5\:m$