Question

Given S. 3t² + 46+9
Find velocity at t=lsec and average velocity between 1
to 4 Sec​

Answer 1

Answer :

1) 10 m/s

2) 19 m/s

Note :

• Velocity = s/t

• Average velocity = ∆s/∆t

= (s2 - s1)/(t2 - t1)

• Instantaneous velocity = ds/dt

Solution :

1) Instantaneous velocity at t = 1 sec :

=> v = ds/dt

=> v = d(3t² + 4t + 9)/dt

=> v = d(3t²)/dt + d(4t)/dt + d(9)/dt

=> v = 3dt²/dt + 4dt/dt + d9/dt

=> v = 3•2t + 4•1 + 0

=> v = 6t + 4

Now ,

• At t = 1 sec , the instantaneous velocity will be ;

→ v = 6•1 + 4

→ v = 6 + 4

→ v = 10 m/s

2) Average velocity between t = 1 sec to t = 4 sec :

We have ,

s = 3t² + 4t + 9

• At t = 1 sec , Initial position will be ;

=> s1 = 3•1² + 4•1 + 9

=> s1 = 3 + 4 + 9

=> s1 = 16 m

• At t = 4 sec , Final position will be ;

=> s2 = 3•4² + 4•4 + 9

=> s2 = 48 + 16 + 9

=> s2 = 73 m

Now ,

• The average velocity between t = 1 sec to t = 4 sec will be ;

=> v = (s2 - s1)/(t2 - t1)

=> v = (73 - 16)/(4 - 1)

=> v = 57/3

=> v = 19 m/s