Question

The speed time graph of a particle moving along the solid curve is shown below. The distance traversed by a particle form t=0 tot=3 is​



Answer is in Image

Answer 1

Answer:

9/4 m (or 2.25 m) (as shown in the figure)

Explanation:

The distance is equal to the rate of change of speed. We should know that wherever rate of change is involved, differential comes into picture.

Therefore if 's' is distance then rate of change of distance will be ds/dt,  where t is time

If v is the speed then

$\frac{ds}{dt} =v$

Now in order to find distance s we need to integrate it in the following way

$ds=vdt\\\implies \int ds=\int vdt$

$\implies s=\int vdt$

Now if we know a little bit of calculus then we should know that if f(x) is a function in x then $\int f(x)dx$ represents area under the curve of the function f(x)

Therefore if velocity is a function of time then $\int vdt$ represents the area under the velocity time graph which is nothing but 's' i.e. the distance covered

Now as given in figure, the area covered by the velocity time graph is

A = (1/2) × 3 × 1.5 sec × m/s

  = 1.5 × 1.5 m

  = 2.25 m