Question

Given a particle's velocity- time graph which is in motion along a line. What is the total distance travelled by the particle till t = 20 sec?

• A. 62.5 m
• B. 37.5 m
• C. 87.5 m
• D. 12.5 m

Answer 1

The correct option is A

62.5 m

Area under the velocity time graph will give us displacement not distance. So in order to get the total distance, v-t graph has to be converted to speed-time graph for the entire motion of the object.

Okay now how to get speed time from velocity time.

All we know that is when velocity becomes negative speed is still positive as speed can never be negative. The magnitude of speed and velocity are always equal.

So in the v-t graph whenever the graph is going down the time axis the speed graph will just be a mirror image of it as shown below.

Total distance or path length = (area under the graph from t = 0 to t = 15s) + (area under t = 15s to t = 20s)

= $(\frac{1}{2}\times 5\times 5)+(5\times 5)+(\frac{1}{2}\times 5\times 5)+(\frac{1}{2}\times 5\times 5)$

= $\frac{3}{2}\times 25+25$

= $\frac{5}{2}\times 25$

= 62.5 m