Question

A body moves along x-axis such that its displacement varies with time s given, x=7+3t+5t^2. The average velocity during 3rd second is :
1) 28m/s
2)42m/s
3)56m/s
4)15m/s

Answer 1

Heya.........!!!!

______________________________


Given in the question :-

• Displacement is given to us as a function of time => x = 5t^2 + 3t + 7

Now we have to take out average velocity during 3rd second .

The main thing in this question is to notice that we have being asked average DURING 3RD SECOND i.e = between 2 and 3 second.

So now ,let us take out the value of displacement during 3rd sec

• Putting ' t ' = 2

=> 5×(2)^2 + 3×(2) + 7
=> 20 + 6 + 7

x1 => 33 m

• Putting ' t ' = 3

=> 5×(3)^2 + 3×3 + 7
=> 45 + 9 + 7

x2 => 61 m

Average velocity = ∆x / ∆t

=> ( 61 - 33 ) / (3 - 2 )

=> 28 / 1

♦ Average Velocity => 28 m/sec .



===============================

Hope It Helps You ☺

Answer 2

▪ Velocity = Displacement/time

Average velocity = dx/dt

To find average velocity at 3rd second , we have find Displacement at 2nd and 3rd second .

• Displacement at 2nd second

》》》 x=7+3t+5t^2

》》x = 7 + (3×2) + 5×(2)^2

》x = 33m

° Displacement at 3rd second

》》》x=7+3t+5t^2

》》 x = 7 + (3×3) + 5×(3)^2

》 x = 61m

☆ Average velocity =dx/dt

》》( 61 - 33)/(3-2)

》 28m/s

♡ Your answer is OPTION [1] 28m/s