Question

The distance travelled by a particle in time t is given by s= (2.5m/s2 )t2. Find the (a) Average speed of the particle during the time 0 to 5 seconds, and (b) the instantaneous speed at t= 5 seconds. (c) t =4 seconds (d) t = 3 seconds
This is the question. I want to know two to three things about what this question tells:-
1. Is the motion uniform ? or the velocity keeps changing ? But how do we know that ?
2. How can the instantaneous velocity at the end of a time interval not be equal to the velocity during the whole time interval ?
Pls. clarify... Thnx...

Answer 1

The Derivates are used in cases you need to find instantaneous velocity, acceleration, displacement etc.

Any average can be found with using a derivative.

Displacement = 2.5t^2

So, average speed =

total displacement/ total time

So, in 5 seconds, the total displacement is

2.5 (5) ^2 = 25×2.5 = 62.5m

Total time = 5 seconds

Therefore, average speed = 62.5/5 = 12.5m/s

Answer 2

Answer: see the attachment below