Question

12 The displacement (in metre) of a particle moving along x-axis is given by
x = 18t + 5t2

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Calculate./i) the instantaneous velocity at t = 2s
(ii)average velocity between t=2s and t = 3s,
(i) indtantaneous acceleration

Answer 1

1...velocity,v= dx/dt = 18+10t
velocity at t=2.... = 18+10(2) = 38 m/ sec
2.... distance travelled in 2 sec = 18(2)+5(2)²=36+20= 56 m
distance travelled in 3 sec = 18(3)+5(3)²=54+45=99m
so the distance travelled between 2sec to 3 sec = 99-56= 43m
so avg velocity= 43/(3-2)= 43 m/s
3....acceleration = dv/dt =10 m/s2

Answer 2

1)
V= dx/dt=18+10t
now at t=2s
V=18+10×2=28m/s
2)
now at
t=3s
V=18+10×3=38m/s
Vav=(38-28)/1=10m/s
3)
a=dv/dt=10m/s^2