Question

the motion of the particle along x axis is given by the equation x=9+5t2,where x is the distance in cm and 't' is time in second.find 1)average velocity during the interval from t=3s to t=5s 2)instantaneous velocity at t=3s.

Answer 1

(1)
Position at t=3 s, x1=9+5(3)2=54 cm    
Position at t=5 s , x2=9+5(5)2=134 cm
The average velocity of an object is the ratio of change is position to time interval in which displacement occurs,i.e
v⃗ =displacementtime interval=∆x⃗ ∆t   =x2−x1t2−t1=134 cm−54 cm5s−3s=802=40 cm/s


(2)  Instantaneous velocity, vi=dxdt=d(9+5t2)dt=10t
                                       at t=3s , vi=10(3)=30cm/s

Answer 2

Answer:

Explanation:

(1)

Position at t=3 s, x1=9+5(3)2=54 cm    

Position at t=5 s , x2=9+5(5)2=134 cm

The average velocity of an object is the ratio of change is position to time interval in which displacement occurs,i.e

v⃗ =displacementtime interval=∆x⃗ ∆t   =x2−x1t2−t1=134 cm−54 cm5s−3s=802=40 cm/s

(2)  Instantaneous velocity, vi=dxdt=d(9+5t2)dt=10t

                                      at t=3s , vi=10(3)=30cm/s