Question

Q. The position of an object moving along x-axis is given by x= a + bt2 where a=8.5m, b=2.5m/s2 and t is measured in seconds. What is its velocity at t=0s and t=2.0s. What is the average velocity b/w t=2.0s and t= 4.0s ?pls reply soon

Answer 1

Hii There!!!

Given,
x = a + bt^2
=> v = 2bt

Velocity at t = 0 is 0

Velocity at t = 2s is = 2×2.5×2 = 10 m/s


Now, At t = 2s

x = 8.5 + 2.5×2^2

x = 18.5m



Similarly, At t = 4s 

x = 8.5 + 2.5×4^2

x = 48.5m


Hence, Average Velocity =  (48.5 - 18.5) / 2

=> 15m/s 


________________________

Hope it helps

Answer 2

x = a + bt²

V = dx/dt ...... ( instantaneous velocity )

V = d( a + bt² ) / dx

V = 2bt²

V = 2 x 2.5 t²

V = 5t² m/s

velocity at t = 0 is. 5 x 0 = 0 m/s

velocity at t = 2 is 5 x 2 = 10 m/s

For t1 = 2

x = a + bt²

= 8.5 + 2.5 x 2 x 2

= 8.5 + 2.5 x 4

= 8.5 + 10

x1 = 18.5 m/s

For t2 = 4

x = a + bt²

= 8.5 + 2.5 x 4 x 4

= 8.5 + 40

x2 = 48.5 m/s

Average velocity = x2 - x1 / t2 - t1

= 48.5 - 18.5 / 4 - 2

= 30 / 2

= 15 m/ s